Warnaar, S. Ole The \(\text{A}_2\) Andrews-Gordon identities and cylindric partitions. (English) Zbl 1518.05009 Trans. Am. Math. Soc., Ser. B 10, 715-765 (2023). MSC: 05A15 05A19 11P84 17B65 33D15 81R10 PDFBibTeX XMLCite \textit{S. O. Warnaar}, Trans. Am. Math. Soc., Ser. B 10, 715--765 (2023; Zbl 1518.05009) Full Text: DOI arXiv
Rains, Eric M.; Warnaar, S. Ole Bounded Littlewood identities. (English) Zbl 1467.05001 Memoirs of the American Mathematical Society 1317. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4690-1/pbk; 978-1-4704-6522-3/ebook). vii, 115 p. (2021). Reviewer: Ioan Tomescu (Bucureşti) MSC: 05-02 05E05 05E10 05A15 05A17 17B67 33D67 11P84 PDFBibTeX XMLCite \textit{E. M. Rains} and \textit{S. O. Warnaar}, Bounded Littlewood identities. Providence, RI: American Mathematical Society (AMS) (2021; Zbl 1467.05001) Full Text: DOI arXiv Link
Bernik, Janez Quasi-filiform Lie algebras of maximum length revisited. (English) Zbl 1469.17010 J. Algebra 541, 146-173 (2020). MSC: 17B30 17B70 PDFBibTeX XMLCite \textit{J. Bernik}, J. Algebra 541, 146--173 (2020; Zbl 1469.17010) Full Text: DOI
Millionshchikov, D. V. Naturally graded Lie algebras of slow growth. (English. Russian original) Zbl 1435.17015 Sb. Math. 210, No. 6, 862-909 (2019); translation from Mat. Sb. 210, No. 6, 111-160 (2019). Reviewer: Andrea Caranti (Trento) MSC: 17B30 PDFBibTeX XMLCite \textit{D. V. Millionshchikov}, Sb. Math. 210, No. 6, 862--909 (2019; Zbl 1435.17015); translation from Mat. Sb. 210, No. 6, 111--160 (2019) Full Text: DOI
Griffin, Michael J.; Ono, Ken; Warnaar, S. Ole A framework of Rogers-Ramanujan identities and their arithmetic properties. (English) Zbl 1405.11140 Duke Math. J. 165, No. 8, 1475-1527 (2016); erratum ibid. 165, No. 12, 2407-2408 (2016). MSC: 11P84 11G16 05E05 05E10 17B67 33D67 PDFBibTeX XMLCite \textit{M. J. Griffin} et al., Duke Math. J. 165, No. 8, 1475--1527 (2016; Zbl 1405.11140) Full Text: DOI arXiv Euclid
Calinescu, C.; Lepowsky, J.; Milas, A. Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types \(A,D,E\). (English) Zbl 1221.17032 J. Algebra 323, No. 1, 167-192 (2010). Reviewer: Stefano Capparelli (Roma) MSC: 17B69 17B67 PDFBibTeX XMLCite \textit{C. Calinescu} et al., J. Algebra 323, No. 1, 167--192 (2010; Zbl 1221.17032) Full Text: DOI arXiv
Calinescu, C.; Lepowsky, J.; Milas, A. Vertex-algebraic structure of the principal subspaces of certain \(A_1^{(1)}\)-modules. II: Higher-level case. (English) Zbl 1184.17013 J. Pure Appl. Algebra 212, No. 8, 1928-1950 (2008). Reviewer: Olaf Ninnemann (Berlin) MSC: 17B69 17B67 PDFBibTeX XMLCite \textit{C. Calinescu} et al., J. Pure Appl. Algebra 212, No. 8, 1928--1950 (2008; Zbl 1184.17013) Full Text: DOI arXiv
Calinescu, C.; Lepowsky, J.; Milas, A. Vertex-algebraic structure of the principal subspaces of certain \(A^{(1)}_1\)-modules. I: Level one case. (English) Zbl 1184.17012 Int. J. Math. 19, No. 1, 71-92 (2008). Reviewer: Olaf Ninnemann (Berlin) MSC: 17B69 05A17 17B67 PDFBibTeX XMLCite \textit{C. Calinescu} et al., Int. J. Math. 19, No. 1, 71--92 (2008; Zbl 1184.17012) Full Text: DOI arXiv
Cook, William J.; Li, Haisheng; Misra, Kailash C. A recurrence relation for characters of highest weight integrable modules for affine Lie algebras. (English) Zbl 1126.17008 Commun. Contemp. Math. 9, No. 2, 121-133 (2007). Reviewer: Stefano Capparelli (Roma) MSC: 17B10 17B67 17B69 PDFBibTeX XMLCite \textit{W. J. Cook} et al., Commun. Contemp. Math. 9, No. 2, 121--133 (2007; Zbl 1126.17008) Full Text: DOI arXiv
Jurisich, Elizabeth A resolution for standard modules of Borcherds Lie algebras. (English) Zbl 1050.17017 J. Pure Appl. Algebra 192, No. 1-3, 149-158 (2004). MSC: 17B65 17B67 17B69 17B55 PDFBibTeX XMLCite \textit{E. Jurisich}, J. Pure Appl. Algebra 192, No. 1--3, 149--158 (2004; Zbl 1050.17017) Full Text: DOI
Leininger, Verne E.; Milne, Stephen C. Expansions for \((q)_\infty^{n^2+2n}\) and basic hypergeometric series in \(U(n)\). (English) Zbl 0936.33010 Discrete Math. 204, No. 1-3, 281-317 (1999). Reviewer: Wolfram Koepf (Leipzig) MSC: 33D70 05E99 05A30 05A19 PDFBibTeX XMLCite \textit{V. E. Leininger} and \textit{S. C. Milne}, Discrete Math. 204, No. 1--3, 281--317 (1999; Zbl 0936.33010) Full Text: DOI
Li, Haisheng Determining fusion rules by \(A(V)\)-modules and bimodules. (English) Zbl 0977.17027 J. Algebra 212, No. 2, 515-556 (1999). Reviewer: Xu Xiaoping (Kowloon) MSC: 17B69 PDFBibTeX XMLCite \textit{H. Li}, J. Algebra 212, No. 2, 515--556 (1999; Zbl 0977.17027) Full Text: DOI
Li, Haisheng An analogue of the Hom functor and a generalized nuclear democracy theorem. (English) Zbl 0956.17017 Duke Math. J. 93, No. 1, 73-114 (1998). Reviewer: Andreas Cap (Wien) MSC: 17B69 PDFBibTeX XMLCite \textit{H. Li}, Duke Math. J. 93, No. 1, 73--114 (1998; Zbl 0956.17017) Full Text: DOI arXiv
Jurisich, E.; Lepowsky, J.; Wilson, R. L. Realizations of the monster Lie algebra. (English) Zbl 0828.17029 Sel. Math., New Ser. 1, No. 1, 129-161 (1995). Reviewer: J.F.Hurley (Storrs) MSC: 17B67 20D08 17B10 17B01 17B68 PDFBibTeX XMLCite \textit{E. Jurisich} et al., Sel. Math., New Ser. 1, No. 1, 129--161 (1995; Zbl 0828.17029) Full Text: DOI arXiv
Fialowski, A. Cohomology of nilpotent subalgebras of affine Lie algebras. (English) Zbl 0808.17012 Proc. Am. Math. Soc. 122, No. 1, 71-77 (1994). MSC: 17B56 17B67 17B30 PDFBibTeX XMLCite \textit{A. Fialowski}, Proc. Am. Math. Soc. 122, No. 1, 71--77 (1994; Zbl 0808.17012) Full Text: DOI
Sthanumoorthy, N.; Tamba, M. A note on a generalization of Macdonald’s identities for \(A_ \ell\) and \(B_ \ell\). (English) Zbl 0822.11037 Proc. Indian Acad. Sci., Math. Sci. 104, No. 2, 377-383 (1994). Reviewer: K.Abdukhalikov (Almaty) MSC: 11F20 17B20 11F22 PDFBibTeX XMLCite \textit{N. Sthanumoorthy} and \textit{M. Tamba}, Proc. Indian Acad. Sci., Math. Sci. 104, No. 2, 377--383 (1994; Zbl 0822.11037) Full Text: DOI
Lian, Bong H. On the classification of simple vertex operator algebras. (English) Zbl 0823.17039 Commun. Math. Phys. 163, No. 2, 307-357 (1994). Reviewer: K.C.Misra (Raleigh) MSC: 17B69 PDFBibTeX XMLCite \textit{B. H. Lian}, Commun. Math. Phys. 163, No. 2, 307--357 (1994; Zbl 0823.17039) Full Text: DOI
Naito, Satoshi The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras. I: The existence of the resolution. (English) Zbl 0822.17022 Publ. Res. Inst. Math. Sci. 29, No. 4, 709-730 (1993). Reviewer: Hiro-Fumi Yamada (Tokyo) MSC: 17B67 PDFBibTeX XMLCite \textit{S. Naito}, Publ. Res. Inst. Math. Sci. 29, No. 4, 709--730 (1993; Zbl 0822.17022) Full Text: DOI
Naito, Satoshi Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras. (English) Zbl 0822.17023 Proc. Japan Acad., Ser. A 69, No. 2, 27-31 (1993). Reviewer: Hiro-Fumi Yamada (Tokyo) MSC: 17B67 PDFBibTeX XMLCite \textit{S. Naito}, Proc. Japan Acad., Ser. A 69, No. 2, 27--31 (1993; Zbl 0822.17023) Full Text: DOI
Naito, Satoshi Kostant’s theorem for a certain class of generalized Kac-Moody algebras. (English) Zbl 0761.17024 Proc. Japan Acad., Ser. A 68, No. 2, 43-47 (1992). Reviewer: S.Naito (Kyoto) MSC: 17B67 17B55 17B56 17B65 PDFBibTeX XMLCite \textit{S. Naito}, Proc. Japan Acad., Ser. A 68, No. 2, 43--47 (1992; Zbl 0761.17024) Full Text: DOI
Liu, Lishi Kostant’s formula for Kac-Moody Lie algebras. (English) Zbl 0779.17024 J. Algebra 149, No. 1, 155-178 (1992). Reviewer: H.Boseck (Greifswald) MSC: 17B67 17B10 PDFBibTeX XMLCite \textit{L. Liu}, J. Algebra 149, No. 1, 155--178 (1992; Zbl 0779.17024) Full Text: DOI
Naito, Satoshi Kostant’s formula for a certian class of generalized Kac-Moody algebras. (English) Zbl 0767.17020 Tôhoku Math. J., II. Ser. 44, No. 4, 567-580 (1992). Reviewer: S.Naito (Shizuoka) MSC: 17B67 17B55 17B56 17B65 PDFBibTeX XMLCite \textit{S. Naito}, Tôhoku Math. J. (2) 44, No. 4, 567--580 (1992; Zbl 0767.17020) Full Text: DOI
Lejbenzon, Z. L. Simple proof of Macdonald’s identities for the series A. (English. Russian original) Zbl 0763.33007 Funct. Anal. Appl. 25, No. 3, 180-183 (1991); translation from Funkts. Anal. Prilozh. 25, No. 3, 19-23 (1991). Reviewer: D.M.Bressoud (University Park) MSC: 33D05 33D80 PDFBibTeX XMLCite \textit{Z. L. Lejbenzon}, Funct. Anal. Appl. 25, No. 3, 180--183 (1991; Zbl 0763.33007); translation from Funkts. Anal. Prilozh. 25, No. 3, 19--23 (1991) Full Text: DOI
Kumar, Shrawan Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras. (English) Zbl 0703.17016 Math. Ann. 286, No. 4, 709-729 (1990). Reviewer: J.Kubarski MSC: 17B67 17B55 17B10 PDFBibTeX XMLCite \textit{S. Kumar}, Math. Ann. 286, No. 4, 709--729 (1990; Zbl 0703.17016) Full Text: DOI EuDML
Milne, S. C. An elementary proof of the Macdonald identities for \(A_{\ell}^{(1)}\). (English) Zbl 0586.33011 Adv. Math. 57, 34-70 (1985). MSC: 33D80 33D15 PDFBibTeX XMLCite \textit{S. C. Milne}, Adv. Math. 57, 34--70 (1985; Zbl 0586.33011) Full Text: DOI
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
Lepowsky, James; Wilson, Robert Lee The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities. (English) Zbl 0577.17009 Invent. Math. 77, 199-290 (1984). Reviewer: L.Vaserstein MSC: 17B65 05A19 PDFBibTeX XMLCite \textit{J. Lepowsky} and \textit{R. L. Wilson}, Invent. Math. 77, 199--290 (1984; Zbl 0577.17009) Full Text: DOI EuDML
Chiu, Sen The homology of Kac-Moody Lie algebras with coefficients in a generalized Verma module. (English) Zbl 0544.17008 J. Algebra 90, 10-17 (1984). Reviewer: A.G.Gejn MSC: 17B55 17B65 17B56 PDFBibTeX XMLCite \textit{S. Chiu}, J. Algebra 90, 10--17 (1984; Zbl 0544.17008) Full Text: DOI
Rocha-Caridi, Alvany; Wallach, Nolan R. Characters of irreducible representations of the Virasoro algebra. (English) Zbl 0503.17008 Math. Z. 185, 1-21 (1984). MSC: 17B65 17B10 PDFBibTeX XMLCite \textit{A. Rocha-Caridi} and \textit{N. R. Wallach}, Math. Z. 185, 1--21 (1984; Zbl 0503.17008) Full Text: DOI EuDML
Meurman, Arne Characters of rank two hyperbolic Lie algebras as functions at quasi- regular cusps. (English) Zbl 0481.17004 J. Algebra 76, 494-504 (1982). MSC: 17B65 PDFBibTeX XMLCite \textit{A. Meurman}, J. Algebra 76, 494--504 (1982; Zbl 0481.17004) Full Text: DOI
Kac, V. G.; Kazhdan, D. A.; Lepowsky, J.; Wilson, R. L. Realization of the basic representations of the Euclidean Lie algebras. (English) Zbl 0476.17003 Adv. Math. 42, 83-112 (1981). MSC: 17B10 17B40 17B65 17B35 17B70 47L90 PDFBibTeX XMLCite \textit{V. G. Kac} et al., Adv. Math. 42, 83--112 (1981; Zbl 0476.17003) Full Text: DOI
Feingold, Alex Jay A hyperbolic GCM Lie algebra and the Fibonacci numbers. (English) Zbl 0446.17009 Proc. Am. Math. Soc. 80, 379-385 (1980). MSC: 17B65 11B37 PDFBibTeX XMLCite \textit{A. J. Feingold}, Proc. Am. Math. Soc. 80, 379--385 (1980; Zbl 0446.17009) Full Text: DOI
Lepowsky, J. Application of the numerator formula to k-rowed plane partitions. (English) Zbl 0425.10015 Adv. Math. 35, 179-194 (1980). MSC: 11P81 17B20 PDFBibTeX XMLCite \textit{J. Lepowsky}, Adv. Math. 35, 179--194 (1980; Zbl 0425.10015) Full Text: DOI
Feingold, Alex J.; Lepowsky, James The Weyl-Kac character formula and power series identities. (English) Zbl 0391.17009 Adv. Math. 29, 271-309 (1978). MSC: 17B65 11P81 PDFBibTeX XMLCite \textit{A. J. Feingold} and \textit{J. Lepowsky}, Adv. Math. 29, 271--309 (1978; Zbl 0391.17009) Full Text: DOI
Lepowsky, James; Wilson, Robert Lee Construction of the affine Lie algebra \(A^{(1)}_1\). (English) Zbl 0388.17006 Commun. Math. Phys. 62, 43-53 (1978). MSC: 17B65 PDFBibTeX XMLCite \textit{J. Lepowsky} and \textit{R. L. Wilson}, Commun. Math. Phys. 62, 43--53 (1978; Zbl 0388.17006) Full Text: DOI
Lepowsky, J.; Milne, S. Lie algebraic approaches to classical partition identities. (English) Zbl 0384.10008 Adv. Math. 29, 15-59 (1978). MSC: 11P81 17B65 05A17 PDFBibTeX XMLCite \textit{J. Lepowsky} and \textit{S. Milne}, Adv. Math. 29, 15--59 (1978; Zbl 0384.10008) Full Text: DOI
Lepowsky, J. Minimal K-types for certain representations of real semisimple groups. (English) Zbl 0382.22007 J. Algebra 51, 173-210 (1978). MSC: 22E46 43A65 PDFBibTeX XMLCite \textit{J. Lepowsky}, J. Algebra 51, 173--210 (1978; Zbl 0382.22007) Full Text: DOI
Lepowsky, J. Generalized Verma modules, the Cartan-Helgason theorem, and the Harish- Chandra homomorphism. (English) Zbl 0381.17005 J. Algebra 49, 470-495 (1977). MSC: 17B35 17B10 22E47 PDFBibTeX XMLCite \textit{J. Lepowsky}, J. Algebra 49, 470--495 (1977; Zbl 0381.17005) Full Text: DOI
Garland, Howard; Lepowsky, James Lie algebra homology and the Macdonald-Kac formulas. (English) Zbl 0358.17015 Invent. Math. 34, 37-76 (1976). Reviewer: Eiichi Abe (Ibaraki) MSC: 17B20 17B10 17B55 17B56 PDFBibTeX XMLCite \textit{H. Garland} and \textit{J. Lepowsky}, Invent. Math. 34, 37--76 (1976; Zbl 0358.17015) Full Text: DOI EuDML