Bakalov, Bojko; Elsinger, Jason; Kac, Victor G.; Todorov, Ivan Orbifolds of lattice vertex algebras. (English) Zbl 07751174 Jpn. J. Math. (3) 18, No. 2, 169-274 (2023). MSC: 17B69 81R10 PDFBibTeX XMLCite \textit{B. Bakalov} et al., Jpn. J. Math. (3) 18, No. 2, 169--274 (2023; Zbl 07751174) Full Text: DOI arXiv
Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo Unitarity of minimal \(W\)-algebras and their representations. I. (English) Zbl 07700880 Commun. Math. Phys. 401, No. 1, 79-145 (2023). MSC: 17B69 17B10 81R10 PDFBibTeX XMLCite \textit{V. G. Kac} et al., Commun. Math. Phys. 401, No. 1, 79--145 (2023; Zbl 07700880) Full Text: DOI arXiv
Kac, Victor G.; Wakimoto, Minoru On free field realization of quantum affine \(W\)-algebras. (English) Zbl 07593339 Commun. Math. Phys. 395, No. 2, 571-600 (2022). MSC: 17B67 81R10 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{M. Wakimoto}, Commun. Math. Phys. 395, No. 2, 571--600 (2022; Zbl 07593339) Full Text: DOI arXiv
Kac, Victor G.; van de Leur, Johan W. Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions. (English) Zbl 1401.14209 Jpn. J. Math. (3) 13, No. 2, 235-271 (2018). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14M15 17B10 17B65 17B67 20G43 22E70 35Q53 35R03 47G30 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{J. W. van de Leur}, Jpn. J. Math. (3) 13, No. 2, 235--271 (2018; Zbl 1401.14209) Full Text: DOI arXiv Link
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele Dirac reduction for Poisson vertex algebras. (English) Zbl 1368.17031 Commun. Math. Phys. 331, No. 3, 1155-1190 (2014). MSC: 17B80 37K10 17B69 81R05 81R10 PDFBibTeX XMLCite \textit{A. De Sole} et al., Commun. Math. Phys. 331, No. 3, 1155--1190 (2014; Zbl 1368.17031) Full Text: DOI arXiv
Kac, Victor G.; Raina, Ashok K.; Rozhkovskaya, Natasha Bombay lectures on highest weight representations of infinite dimensional Lie algebras. 2nd ed. (English) Zbl 1294.17021 Advanced Series in Mathematical Physics 29. Hackensack, NJ: World Scientific (ISBN 978-981-4522-18-2/hbk; 978-981-4522-19-9/pbk; 978-981-4522-21-2/ebook). xii, 237 p. (2013). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B68 17-02 17B69 17B67 17B65 17B80 37K40 81R10 81T40 PDFBibTeX XMLCite \textit{V. G. Kac} et al., Bombay lectures on highest weight representations of infinite dimensional Lie algebras. 2nd ed. Hackensack, NJ: World Scientific (2013; Zbl 1294.17021) Full Text: DOI
Bakalov, B.; Kac, V. G. Generalized vertex algebras. (English) Zbl 1241.17029 Bulg. J. Phys. 33, No. S2, 3-25 (2006). MSC: 17B69 81R10 PDFBibTeX XMLCite \textit{B. Bakalov} and \textit{V. G. Kac}, Bulg. J. Phys. 33, No. S2, 3--25 (2006; Zbl 1241.17029) Full Text: arXiv
Boyallian, Carina; Kac, Victor G.; Liberati, Jose I.; Rudakov, Alexei Representations of simple finite Lie conformal superalgebras of type \(W\) and \(S\). (English) Zbl 1111.17001 J. Math. Phys. 47, No. 4, 043513, 25 p. (2006). Reviewer: Olaf Ninnemann (Uffing am Staffelsee) MSC: 17B69 17B65 81R10 PDFBibTeX XMLCite \textit{C. Boyallian} et al., J. Math. Phys. 47, No. 4, 043513, 25 p. (2006; Zbl 1111.17001) Full Text: DOI arXiv
Fattori, Davide; Kac, Victor G.; Retakh, Alexander Structure theory of finite Lie conformal superalgebras. (English) Zbl 1229.17027 Doebner, H.-D.(ed.) et al., Lie theory and its applications in physics V. Proceedings of the 5th international workshop, Varna, Bulgaria, June 16–22, 2003. Hackensack, NJ: World Scientific (ISBN 981-238-936-9). 27-63 (2005). Reviewer: Olaf Ninnemann (Berlin) MSC: 17B68 81R10 81T40 PDFBibTeX XMLCite \textit{D. Fattori} et al., in: Lie theory and its applications in physics V. Proceedings of the 5th international workshop, Varna, Bulgaria, June 16--22, 2003. Hackensack, NJ: World Scientific. 27--63 (2005; Zbl 1229.17027) Full Text: DOI arXiv
Kac, Victor G.; Wakimoto, Minoru Quantum reduction in the twisted case. (English) Zbl 1132.17306 Kulish, Petr P. (ed.) et al., Infinite dimensional algebras and quantum integrable systems. Papers from the 14th international congress on mathematical physics satellite workshop, Faro, Portugal, July 21–25, 2003. Basel: Birkhäuser (ISBN 3-7643-7215-X/hbk). Progress in Mathematics 237, 89-131 (2005). MSC: 17B69 17B68 81R10 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{M. Wakimoto}, Prog. Math. 237, 89--131 (2005; Zbl 1132.17306) Full Text: arXiv
De Sole, Alberto; Kac, Victor G. Freely generated vertex algebras and nonlinear Lie conformal algebras. (English) Zbl 1104.17016 Commun. Math. Phys. 254, No. 3, 659-694 (2005). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B69 81R10 PDFBibTeX XMLCite \textit{A. De Sole} and \textit{V. G. Kac}, Commun. Math. Phys. 254, No. 3, 659--694 (2005; Zbl 1104.17016) Full Text: DOI arXiv
Kac, Victor G.; Wakimoto, Minoru Quantum reduction and representation theory of superconformal algebras. (English) Zbl 1049.17025 Adv. Math. 185, No. 2, 400-458 (2004), corrigendum 193, No. 2, 453-455 (2005). Reviewer: Antun Milas (Albany) MSC: 17B69 17B68 81R10 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{M. Wakimoto}, Adv. Math. 185, No. 2, 400--458 (2004; Zbl 1049.17025) Full Text: DOI arXiv
Kac, V. G.; van de Leur, J. W. The \(n\)-component KP hierarchy and representation theory. (English) Zbl 1062.37071 J. Math. Phys. 44, No. 8, 3245-3293 (2003). MSC: 37K10 35Q53 37K30 81R12 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{J. W. van de Leur}, J. Math. Phys. 44, No. 8, 3245--3293 (2003; Zbl 1062.37071) Full Text: DOI arXiv
Kac, Victor; Roan, Shi-Shyr; Wakimoto, Minoru Quantum reduction for affine superalgebras. (English) Zbl 1106.17026 Commun. Math. Phys. 241, No. 2-3, 307-342 (2003). MSC: 17B65 17B37 17B67 81R10 81T70 PDFBibTeX XMLCite \textit{V. Kac} et al., Commun. Math. Phys. 241, No. 2--3, 307--342 (2003; Zbl 1106.17026) Full Text: DOI arXiv
Boyallian, Carina; Kac, Victor G.; Liberati, Jose I. On the classification of subalgebras of \(\text{Cend}_N\) and \(\text{gc}_N\). (English) Zbl 1034.17018 J. Algebra 260, No. 1, 32-63 (2003). Reviewer: Yong-Qing Chen (Shenzhen) MSC: 17B10 17B68 17B81 81R10 PDFBibTeX XMLCite \textit{C. Boyallian} et al., J. Algebra 260, No. 1, 32--63 (2003; Zbl 1034.17018) Full Text: DOI
Kac, Victor G. Classification of supersymmetries. (English) Zbl 1057.17021 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20–28, 2002. Vol. I: Plenary lectures and ceremonies. Beijing: Higher Education Press; Singapore: World Scientific/distributor (ISBN 7-04-008690-5/3 vol. set). 319-344 (2002). MSC: 17B68 81R10 81T60 PDFBibTeX XMLCite \textit{V. G. Kac}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. I: Plenary lectures and ceremonies. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 319--344 (2002; Zbl 1057.17021) Full Text: arXiv
Fattori, Davide; Kac, Victor G. Classification of finite simple Lie conformal superalgebras. (English) Zbl 1050.17023 J. Algebra 258, No. 1, 23-59 (2002). Reviewer: Yucai Su (Shanghai) MSC: 17B68 81R10 17B20 PDFBibTeX XMLCite \textit{D. Fattori} and \textit{V. G. Kac}, J. Algebra 258, No. 1, 23--59 (2002; Zbl 1050.17023) Full Text: DOI arXiv
Kac, Victor G. Erratum: Superconformal algebras and transitive group actions on quadratics. (English) Zbl 1040.17500 Commun. Math. Phys. 217, No. 3, 697-698 (2001). MSC: 17B69 81R10 PDFBibTeX XMLCite \textit{V. G. Kac}, Commun. Math. Phys. 217, No. 3, 697--698 (2001; Zbl 1040.17500) Full Text: DOI
Kac, Victor G. Classification of infinite-dimensional simple groups of supersymmetries and quantum field theory. Special volume of the journal Geometric and Functional Analysis. (English) Zbl 0985.57002 Alon, N. (ed.) et al., GAFA 2000. Visions in mathematics–Towards 2000. Proceedings of a meeting, Tel Aviv, Israel, August 25-September 3, 1999. Part I. Basel: Birkhäuser, 162-183 (2000). Reviewer: Chandra Shekhar Sharma (London) MSC: 57-02 81-02 22E70 81R10 81P10 17B81 81T99 PDFBibTeX XMLCite \textit{V. G. Kac}, in: GAFA 2000. Visions in mathematics---Towards 2000. Proceedings of a meeting, Tel Aviv, Israel, August 25--September 3, 1999. Part I. Basel: Birkhäuser. 162--183 (2000; Zbl 0985.57002) Full Text: arXiv
Cheng, Shun-Jen; Kac, Victor G.; Wakimoto, Minoru Extensions of Neveu-Schwarz conformal modules. (English) Zbl 0987.81037 J. Math. Phys. 41, No. 4, 2271-2294 (2000). MSC: 81R10 81T40 17B68 PDFBibTeX XMLCite \textit{S.-J. Cheng} et al., J. Math. Phys. 41, No. 4, 2271--2294 (2000; Zbl 0987.81037) Full Text: DOI
Kac, Victor G.; Liberati, José I. Unitary quasi-finite representations of \(W_\infty\). (English) Zbl 0974.17033 Lett. Math. Phys. 53, No. 1, 11-27 (2000). Reviewer: M.Primc (Zagreb) MSC: 17B68 81R10 17B70 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{J. I. Liberati}, Lett. Math. Phys. 53, No. 1, 11--27 (2000; Zbl 0974.17033) Full Text: DOI
Kac, Victor G. Formal distribution algebras and conformal algebras. (English) Zbl 1253.17002 De Wit, David (ed.) et al., 12th international congress of mathematical physics (ICMP’97). Proceedings of the congress held in Brisbane, Australia, July 13–19, 1997. Cambridge, MA: International Press (ISBN 1-57146-055-1). 80-97 (1999). MSC: 17-02 17B70 17B68 81R10 PDFBibTeX XMLCite \textit{V. G. Kac}, in: 12th international congress of mathematical physics (ICMP'97). Proceedings of the congress held in Brisbane, Australia, July 13--19, 1997. Cambridge, MA: International Press. 80--97 (1999; Zbl 1253.17002) Full Text: arXiv
Bakalov, Bojko; Kac, Victor G.; Voronov, Alexander A. Cohomology of conformal algebras. (English) Zbl 0959.17018 Commun. Math. Phys. 200, No. 3, 561-598 (1999). Reviewer: Alexander Rudy (Minsk) MSC: 17B56 17B68 81R10 PDFBibTeX XMLCite \textit{B. Bakalov} et al., Commun. Math. Phys. 200, No. 3, 561--598 (1999; Zbl 0959.17018) Full Text: DOI arXiv
Kac, Victor \(W\)-algebras and quantum Hall effect. (English) Zbl 0937.17016 Kang, Ming-Chang (ed.), Lectures in algebra and geometry. Proceedings of the international conference on algebra and geometry, National Taiwan University, Taipei, Taiwan, December 26-30, 1995. Cambridge, MA: International Press. 75-81 (1998). MSC: 17B66 81V70 81R10 PDFBibTeX XMLCite \textit{V. Kac}, in: Lectures in algebra and geometry. Proceedings of the international conference on algebra and geometry, National Taiwan University, Taipei, Taiwan, December 26--30, 1995. Cambridge, MA: International Press. 75--81 (1998; Zbl 0937.17016)
Golenishcheva-Kutuzova, Maria I.; Kac, Victor G. \(\Gamma\)-conformal algebras. (English) Zbl 1031.81527 J. Math. Phys. 39, No. 4, 2290-2305 (1998). MSC: 81R10 17B65 PDFBibTeX XMLCite \textit{M. I. Golenishcheva-Kutuzova} and \textit{V. G. Kac}, J. Math. Phys. 39, No. 4, 2290--2305 (1998; Zbl 1031.81527) Full Text: DOI arXiv
Cheng, Shun-Jen; Kac, Victor G.; Wakimoto, Minoru Extensions of conformal modules. (English) Zbl 0937.17019 Kashiwara, Masaki (ed.) et al., Topological field theory, primitive forms and related topics. Proceedings of the 38th Taniguchi symposium, Kyoto, Japan, December 9-13, 1996 and the RIMS symposium with the same title, Kyoto, Japan, December 16-19, 1996. Boston, MA: Birkhäuser. Prog. Math. 160, 79-129 (1998). Reviewer: Dražen Adamović (Zagreb) MSC: 17B68 81R10 17B69 PDFBibTeX XMLCite \textit{S.-J. Cheng} et al., Prog. Math. 160, 79--129 (1998; Zbl 0937.17019) Full Text: arXiv
D’Andrea, Alessandro; Kac, Victor G. Structure theory of finite conformal algebras. (English) Zbl 0918.17019 Sel. Math., New Ser. 4, No. 3, 377-418 (1998). Reviewer: Dražen Adamović (Zagreb) MSC: 17B68 81R10 17B69 PDFBibTeX XMLCite \textit{A. D'Andrea} and \textit{V. G. Kac}, Sel. Math., New Ser. 4, No. 3, 377--418 (1998; Zbl 0918.17019) Full Text: DOI Link
Kac, Victor G.; Wang, Weiqiang; Yan, Catherine H. Quasifinite representations of classical Lie subalgebras of \({\mathcal W}_{1+\infty}\). (English) Zbl 0938.17018 Adv. Math. 139, No. 1, 56-140 (1998). Reviewer: Volodymyr Mazorchuk (Kyïv) MSC: 17B68 81R10 PDFBibTeX XMLCite \textit{V. G. Kac} et al., Adv. Math. 139, No. 1, 56--140 (1998; Zbl 0938.17018) Full Text: DOI arXiv
Kac, Victor G. Classification of infinite-dimensional simple linearly compact Lie superalgebras. (English) Zbl 0929.17026 Adv. Math. 139, No. 1, 1-55 (1998). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 17B66 17B65 81R10 PDFBibTeX XMLCite \textit{V. G. Kac}, Adv. Math. 139, No. 1, 1--55 (1998; Zbl 0929.17026) Full Text: DOI Link
Cheng, Shun-Jen; Kac, Victor G. Conformal modules. (English) Zbl 1022.17018 Asian J. Math. 1, No. 1, 181-193 (1997); erratum 2, No. 1, 153-156 (1998). MSC: 17B68 81R10 17B66 PDFBibTeX XMLCite \textit{S.-J. Cheng} and \textit{V. G. Kac}, Asian J. Math. 1, No. 1, 181--193 (1997; Zbl 1022.17018) Full Text: DOI arXiv
Kac, Victor G.; Todorov, Ivan T. Affine orbifolds and rational conformal field theory extensions of \(W_{1+\infty}\). (English) Zbl 0904.17021 Commun. Math. Phys. 190, No. 1, 57-111 (1997). Reviewer: M.Schlichenmaier (Mannheim) MSC: 17B67 11F22 81R10 81T40 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{I. T. Todorov}, Commun. Math. Phys. 190, No. 1, 57--111 (1997; Zbl 0904.17021) Full Text: DOI arXiv
Kac, Victor G. Superconformal algebras and transitive group actions on quadrics. (English) Zbl 0886.17021 Commun. Math. Phys. 186, No. 1, 233-252 (1997). Reviewer: A.N.Pressley (London) MSC: 17B69 81R10 PDFBibTeX XMLCite \textit{V. G. Kac}, Commun. Math. Phys. 186, No. 1, 233--252 (1997; Zbl 0886.17021) Full Text: DOI
Cheng, Shun-Jen; Kac, Victor G. A new \(N=6\) superconformal algebra. (English) Zbl 0906.17020 Commun. Math. Phys. 186, No. 1, 219-231 (1997). MSC: 17B68 81R10 17B69 PDFBibTeX XMLCite \textit{S.-J. Cheng} and \textit{V. G. Kac}, Commun. Math. Phys. 186, No. 1, 219--231 (1997; Zbl 0906.17020) Full Text: DOI
Frenkel, Edward; Kac, Victor; Radul, Andrey; Wang, Weiqiang \({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\). (English) Zbl 0838.17028 Commun. Math. Phys. 170, No. 2, 337-357 (1995). Reviewer: M.Schlichenmaier (Mannheim) MSC: 17B68 17B69 81R10 81T40 17B70 17B67 PDFBibTeX XMLCite \textit{E. Frenkel} et al., Commun. Math. Phys. 170, No. 2, 337--357 (1995; Zbl 0838.17028) Full Text: DOI arXiv
Kac, V. G.; Wang, S. P. On automorphisms of Kac-Moody algebras and groups. (English) Zbl 0851.17026 Adv. Math. 92, No. 2, 129-195 (1992). Reviewer: O.Ninnemann (Berlin) MSC: 17B67 22E65 17B40 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{S. P. Wang}, Adv. Math. 92, No. 2, 129--195 (1992; Zbl 0851.17026) Full Text: DOI
Kac, Victor G. Modular invariance in mathematics and physics. (English) Zbl 1073.17505 Browder, Felix E. (ed.), Mathematics into the twenty-first century. Proceedings of the AMS centennial symposium, Providence, RI, USA, August 8–12, 1988. Providence, RI: American Mathematical Society (ISBN 0-8218-0167-8). Am. Math. Soc. Centen. Publ. 2, 337-350 (1992). Reviewer: Jeffrey S. Joel (Bloomington) MSC: 17B67 11F22 17B68 17B81 37J99 81R10 PDFBibTeX XMLCite \textit{V. G. Kac}, Am. Math. Soc. Centen. Publ. 2, 337--350 (1992; Zbl 1073.17505)
Kac, Victor G. Infinite dimensional Lie algebras. 3rd ed. (English) Zbl 0716.17022 Cambridge etc.: Cambridge University Press. xxi, 400 p. £40.00; $ 69.50 (1990). Reviewer: Helmut Boseck (Greifswald) MSC: 17B67 17-02 17B65 17B68 17B69 81R10 PDFBibTeX XMLCite \textit{V. G. Kac}, Infinite dimensional Lie algebras. 3rd ed. Cambridge etc.: Cambridge University Press (1990; Zbl 0716.17022)
Kac, V. G.; van de Leur, J. W. Super boson-fermion correspondence of type B. (English) Zbl 0748.17021 Infinite dimensional Lie algebras and groups, Proc. Conf., Marseille/Fr. 1988, Adv. Ser. Math. Phys. 7, 369-406 (1989). MSC: 17B67 17B70 37J35 37K10 17B81 81R10 35Q53 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{J. W. van de Leur}, Adv. Ser. Math. Phys. 7, 369--406 (1989; Zbl 0748.17021)
De Concini, C.; Kac, V. G.; Kazhdan, D. A. Boson-fermion correspondence over \(\mathbb{Z}\). (English) Zbl 0744.17027 Infinite dimensional Lie algebras and groups, Proc. Conf., Marseille/Fr. 1988, Adv. Ser. Math. Phys. 7, 124-137 (1989). MSC: 17B67 81R10 17B45 PDFBibTeX XMLCite \textit{C. De Concini} et al., Adv. Ser. Math. Phys. 7, 124--137 (1989; Zbl 0744.17027)
Kac, Victor G. (ed.) Infinite dimensional Lie algebras and groups. Proceedings of the conference, held at CIRM, Luminy, Marseille, France, July 4-8, 1988. (English) Zbl 0741.00064 Advanced Series in Mathematical Physics. 7. London etc.: World Scientific. viii, 625 p. (1989). MSC: 00B25 17-06 22-06 PDFBibTeX XMLCite \textit{V. G. Kac} (ed.), Infinite dimensional Lie algebras and groups. Proceedings of the conference, held at CIRM, Luminy, Marseille, France, July 4-8, 1988. London etc.: World Scientific (1989; Zbl 0741.00064)
Arbarello, E.; De Concini, C.; Kac, V. G. The infinite wedge representation and the reciprocity law for algebraic curves. (English) Zbl 0699.22028 Theta functions, Proc. 35th Summer Res. Inst. Bowdoin Coll., Brunswick/ME 1987, Proc. Symp. Pure Math. 49, Pt. 1, 171-190 (1989). Reviewer: H.Reitberger MSC: 22E65 14H05 14F10 11R56 17B65 PDFBibTeX XML
Kac, V. G.; van de Leur, J. W. On classification of superconformal algebras. (English) Zbl 0938.17500 Gates, S. J. jun. (ed.) et al., Strings ’88. Proceedings of a workshop, May 24-28, 1988 at University of Maryland, at College Park, Baltimore, MD, USA. Singapore etc.: World Scientific. 77-106 (1989). MSC: 17B68 81R10 81T40 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{J. W. van de Leur}, in: Strings '88. Proceedings of a workshop, May 24-28, 1988 at the University of Maryland, at College Park, Baltimore, MD, USA. Singapore etc.: World Scientific. 77--106 (1989; Zbl 0938.17500)
Kac, Victor G.; Peterson, Dale H. On geometric invariant theory for infinite-dimensional groups. (English) Zbl 0652.17011 Algebraic groups, Proc. Symp., Utrecht/Neth. 1986, Lect. Notes Math. 1271, 109-142 (1987). Reviewer: F.Levstein MSC: 17B67 22E65 20E34 PDFBibTeX XML
Kac, V. G.; Peterson, D. H. Lectures on the infinite wedge-representation and the MKP hierarchy. (English) Zbl 0638.35070 Systèmes dynamiques non linéaires: intégrabilité et comportement qualitatif, Sémin. Math. Supér., Sémin. Sci. OTAN (NATO Adv. Study Inst.) 102, 141-183 (1986). Reviewer: G.F.Post MSC: 35Q99 17B67 22E65 14M15 35A30 PDFBibTeX XML
Kac, Victor G.; Peterson, Dale H. 112 constructions of the basic representation of the loop group of \(E_ 8\). (English) Zbl 0642.17013 Anomalies, geometry, topology, Symp. Chicago/Ill. 1985, 276-298 (1985). MSC: 17B67 17B10 22E65 PDFBibTeX XML
Kac, V. G.; Peterson, D. H. Defining relations of certain infinite dimensional groups. (English) Zbl 0625.22014 Élie Cartan et les mathématiques d’aujourd’hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Astérisque, No.Hors Sér. 1985, 165-208 (1985). Reviewer: A.Verona MSC: 22E65 17B67 PDFBibTeX XML
Kac, Victor G. Constructing groups associated to infinite-dimensional Lie algebras. (English) Zbl 0614.22006 Infinite dimensional groups with applications, Publ., Math. Sci. Res. Inst. 4, 167-216 (1985). Reviewer: I.V.Chekalov MSC: 22E65 17B67 17B65 22E60 PDFBibTeX XML
Kac, V. (ed.) Infinite dimensional groups with applications. (Dedicated to the memory of Claude Chevalley). (English) Zbl 0577.00010 Mathematical Sciences Research Institute Publications, Vol. 4. New York etc.: Springer-Verlag. X, 380 p. DM 98.00 (1985). MSC: 00Bxx 22-06 17-06 58-06 PDFBibTeX XML
Kac, Victor G. Infinite dimensional Lie algebras. 2nd ed. (English) Zbl 0574.17010 Cambridge etc.: Cambridge University Press. XVII, 280 p. £25.00; $ 24.95 (1985). Reviewer: O.Ninnemann MSC: 17B65 22-01 17-02 05A19 11P81 11F11 17-01 17B10 22E65 35Q99 37J99 PDFBibTeX XML
Kac, Victor G.; Peterson, Dale H. Infinite-dimensional Lie algebras, theta functions and modular forms. (English) Zbl 0584.17007 Adv. Math. 53, 125-264 (1984). Reviewer: James F. Hurley (Storrs) MSC: 17B65 17B10 11F11 11F70 22E65 14K25 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{D. H. Peterson}, Adv. Math. 53, 125--264 (1984; Zbl 0584.17007) Full Text: DOI Backlinks: MO
Kac, V. G.; Peterson, D. H. Unitary structure in representations of infinite-dimensional groups and a convexity theorem. (English) Zbl 0534.17008 Invent. Math. 76, 1-14 (1984). Reviewer: Werner Kugler (Berlin) MSC: 17B65 17B10 22E65 17B15 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{D. H. Peterson}, Invent. Math. 76, 1--14 (1984; Zbl 0534.17008) Full Text: DOI EuDML
Kac, Victor G.; Peterson, Dale H. Regular functions on certain infinite-dimensional groups. (English) Zbl 0578.17014 Arithmetic and geometry, Pap. dedic. I. R. Shafarevich, Vol. II: Geometry, Prog. Math. 36, 141-166 (1983). Reviewer: Vladimir L. Popov (Moskva) MSC: 17B65 22E65 17B10 13F15 PDFBibTeX XML
Kac, Victor G. Infinite dimensional Lie algebras. An introduction. (English) Zbl 0537.17001 Progress in Mathematics, Vol. 44. Boston - Basel - Stuttgart: Birkhäuser. xvi, 245 p. DM 58.00 (1983). Reviewer: B. Ju. Weisfeiler MSC: 17B67 17-01 17-02 22E67 17B10 22-01 05A19 11P81 11F22 35Q53 37K10 37K30 PDFBibTeX XML
Peterson, Dale H.; Kac, Victor G. Infinite flag varieties and conjugacy theorems. (English) Zbl 0512.17008 Proc. Natl. Acad. Sci. USA 80, 1778-1782 (1983). MSC: 17B65 17B10 17B40 22E46 PDFBibTeX XMLCite \textit{D. H. Peterson} and \textit{V. G. Kac}, Proc. Natl. Acad. Sci. USA 80, 1778--1782 (1983; Zbl 0512.17008) Full Text: DOI
Deodhar, Vinay V.; Gabber, Ofer; Kac, Victor Structure of some categories of representations of infinite-dimensional Lie algebras. (English) Zbl 0491.17008 Adv. Math. 45, 92-116 (1982). MSC: 17B65 17B10 22E47 PDFBibTeX XMLCite \textit{V. V. Deodhar} et al., Adv. Math. 45, 92--116 (1982; Zbl 0491.17008) Full Text: DOI
Kac, Victor G.; Peterson, Dale H. Spin and wedge representations of infinite-dimensional Lie algebras and groups. (English) Zbl 0469.22016 Proc. Natl. Acad. Sci. USA 78, 3308-3312 (1981). MSC: 22E65 81R10 17B65 22E50 17B10 22E70 PDFBibTeX XMLCite \textit{V. G. Kac} and \textit{D. H. Peterson}, Proc. Natl. Acad. Sci. USA 78, 3308--3312 (1981; Zbl 0469.22016) Full Text: DOI
Kac, V. G. Contravariant form for infinite-dimensional Lie algebras and superalgebras. (English) Zbl 0574.17002 Group theoretical methods in physics, Lect. Notes Phys. 94, 441-445 (1979). MSC: 17B68 17B10 81R10 PDFBibTeX XML