Frenkel, Edward; Koroteev, Peter; Sage, Daniel S.; Zeitlin, Anton M. \(q\)-opers, \(QQ\)-systems, and Bethe Ansatz. (English) Zbl 07815184 J. Eur. Math. Soc. (JEMS) 26, No. 1, 355-405 (2024). MSC: 82B23 82D40 17B80 14D24 81R50 22E10 39A06 37K35 PDFBibTeX XMLCite \textit{E. Frenkel} et al., J. Eur. Math. Soc. (JEMS) 26, No. 1, 355--405 (2024; Zbl 07815184) Full Text: DOI arXiv
Chirvasitu, Alexandru Straightening Banach-Lie-group-valued almost-cocycles. arXiv:2401.14929 Preprint, arXiv:2401.14929 [math.GR] (2024). MSC: 22E65 22C05 58B25 46E50 20J06 58C15 22E66 22D12 39B82 46G20 22E41 BibTeX Cite \textit{A. Chirvasitu}, ``Straightening Banach-Lie-group-valued almost-cocycles'', Preprint, arXiv:2401.14929 [math.GR] (2024) Full Text: arXiv OA License
Igonin, S.; Konstantinou-Rizos, S. Local Yang-Baxter correspondences and set-theoretical solutions to the Zamolodchikov tetrahedron equation. (English) Zbl 1516.37076 J. Phys. A, Math. Theor. 56, No. 27, Article ID 275202, 18 p. (2023). MSC: 37J70 37K35 39A36 35Q55 16T25 PDFBibTeX XMLCite \textit{S. Igonin} and \textit{S. Konstantinou-Rizos}, J. Phys. A, Math. Theor. 56, No. 27, Article ID 275202, 18 p. (2023; Zbl 1516.37076) Full Text: DOI arXiv
Stukopin, V. A. Quasitriangular structures on the super-Yangian and quantum loop superalgebra, and difference equations. (English. Russian original) Zbl 1516.17016 Theor. Math. Phys. 213, No. 1, 1423-1440 (2022); translation from Teor. Mat. Fiz. 213, No. 1, 129-148 (2022). MSC: 17B37 17B67 17B10 39A10 16T25 81R10 PDFBibTeX XMLCite \textit{V. A. Stukopin}, Theor. Math. Phys. 213, No. 1, 1423--1440 (2022; Zbl 1516.17016); translation from Teor. Mat. Fiz. 213, No. 1, 129--148 (2022) Full Text: DOI
Tarasov, Vitaly; Uvarov, Filipp Duality for Knizhnik-Zamolodchikov and dynamical operators. (English) Zbl 1487.17035 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 035, 10 p. (2020). MSC: 17B37 37K30 39A12 81R10 81R50 PDFBibTeX XMLCite \textit{V. Tarasov} and \textit{F. Uvarov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 035, 10 p. (2020; Zbl 1487.17035) Full Text: DOI arXiv
Iwao, Shinsuke Jeu de taquin, uniqueness of rectification and ultradiscrete KP. (English) Zbl 1481.37090 J. Integrable Syst. 4, Article ID xyz012, 25 p. (2019). MSC: 37K60 37K30 39A36 05E16 14T90 PDFBibTeX XMLCite \textit{S. Iwao}, J. Integrable Syst. 4, Article ID xyz012, 25 p. (2019; Zbl 1481.37090) Full Text: DOI arXiv
Konstantinou-Rizos, S.; Kouloukas, T. E. A noncommutative discrete potential KdV lift. (English) Zbl 1395.37046 J. Math. Phys. 59, No. 6, 063506, 13 p. (2018). Reviewer: Eszter Gselmann (Debrecen) MSC: 37K10 81R12 16T25 37K35 37K60 39A14 PDFBibTeX XMLCite \textit{S. Konstantinou-Rizos} and \textit{T. E. Kouloukas}, J. Math. Phys. 59, No. 6, 063506, 13 p. (2018; Zbl 1395.37046) Full Text: DOI arXiv Link
Konno, Hitoshi Elliptic weight functions and elliptic \(q\)-KZ equation. (English) Zbl 1397.37083 J. Integrable Syst. 2, Article ID xyx011, 43 p. (2017). MSC: 37K30 39A13 37K10 17B37 16T05 81R10 33C60 PDFBibTeX XMLCite \textit{H. Konno}, J. Integrable Syst. 2, Article ID xyx011, 43 p. (2017; Zbl 1397.37083) Full Text: arXiv
Bertram, Wolfgang Lie calculus. (English) Zbl 1431.18006 Fialowski, Alice (ed.) et al., 50th Seminar “Sophus Lie”, Będlewo, Poland, September 26 – October 1, 2016. Dedicated to Professor Karl Heinrich Hofmann on the occasion of his 85th birthday. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 113, 59-85 (2017). MSC: 18F15 20L05 22E65 39A12 58C20 97I40 PDFBibTeX XMLCite \textit{W. Bertram}, Banach Cent. Publ. 113, 59--85 (2017; Zbl 1431.18006) Full Text: DOI arXiv
Gordina, Maria An application of a functional inequality to quasi-invariance in infinite dimensions. (English) Zbl 1384.39016 Carlen, Eric (ed.) et al., Convexity and concentration. New York, NY: Springer (ISBN 978-1-4939-7004-9/hbk; 978-1-4939-7005-6/ebook). The IMA Volumes in Mathematics and its Applications 161, 251-266 (2017). Reviewer: Tomasz Zgraja (Bielsko-Biała) MSC: 39B62 22E65 22E30 22E45 60B15 60H05 PDFBibTeX XMLCite \textit{M. Gordina}, IMA Vol. Math. Appl. 161, 251--266 (2017; Zbl 1384.39016) Full Text: DOI arXiv
Berkeley, George; Mikhailov, Alexander V.; Xenitidis, Pavlos Darboux transformations with tetrahedral reduction group and related integrable systems. (English) Zbl 1349.37063 J. Math. Phys. 57, No. 9, 092701, 15 p. (2016). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37K10 37K35 35Q55 39A14 17B45 37L20 70G65 PDFBibTeX XMLCite \textit{G. Berkeley} et al., J. Math. Phys. 57, No. 9, 092701, 15 p. (2016; Zbl 1349.37063) Full Text: DOI arXiv Link
Suzuki, Takao A \(q\)-analogue of the Drinfeld-Sokolov hierarchy of type \(A\) and \(q\)-Painlevé system. (English) Zbl 1346.39010 Dzhamay, Anton (ed.) et al., Algebraic and analytic aspects of integrable systems and Painlevé equations. AMS special session, Baltimore, MD, USA, January 18, 2014. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1654-6/pbk; 978-1-4704-2779-5/ebook). Contemporary Mathematics 651, 25-38 (2015). MSC: 39A12 39A13 34M55 37K10 37K35 33D15 PDFBibTeX XMLCite \textit{T. Suzuki}, Contemp. Math. 651, 25--38 (2015; Zbl 1346.39010) Full Text: DOI arXiv
Konstantinou-Rizos, S.; Mikhailov, A. V.; Xenitidis, P. Reduction groups and related integrable difference systems of nonlinear Schrödinger type. (English) Zbl 1328.35213 J. Math. Phys. 56, No. 8, 082701, 21 p. (2015). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 39A12 37K35 PDFBibTeX XMLCite \textit{S. Konstantinou-Rizos} et al., J. Math. Phys. 56, No. 8, 082701, 21 p. (2015; Zbl 1328.35213) Full Text: DOI arXiv
Tsuda, Teruhisa Tropical Weyl group action via point configurations and \(\tau\)-functions of the \(q\)-Painlevé equations. (English) Zbl 1118.39007 Lett. Math. Phys. 77, No. 1, 21-30 (2006). Reviewer: Ahmed Hegazi (Mansoura) MSC: 39A13 34M55 37K20 37K35 17B20 20F55 PDFBibTeX XMLCite \textit{T. Tsuda}, Lett. Math. Phys. 77, No. 1, 21--30 (2006; Zbl 1118.39007) Full Text: DOI
Damianou, Pantelis A. On the bi-Hamiltonian structure of Bogoyavlensky-Toda lattices. (English) Zbl 1052.37045 Nonlinearity 17, No. 2, 397-413 (2004). Reviewer: Dimitar A. Kolev (Sofia) MSC: 37J35 22E70 70H06 39A12 37K10 37K60 PDFBibTeX XMLCite \textit{P. A. Damianou}, Nonlinearity 17, No. 2, 397--413 (2004; Zbl 1052.37045) Full Text: DOI
Dimakis, Aristophanes; Müller-Hoissen, Folkert On generalized Lotka-Volterra lattices. (English) Zbl 1047.37054 Czech. J. Phys. 52, No. 11, 1187-1193 (2002). MSC: 37K60 37K35 39A12 92D25 81R12 PDFBibTeX XMLCite \textit{A. Dimakis} and \textit{F. Müller-Hoissen}, Czech. J. Phys. 52, No. 11, 1187--1193 (2002; Zbl 1047.37054) Full Text: DOI arXiv
Kikuchi, Tetsuya Diagonalization of the elliptic Macdonald-Ruijsenaars difference system of type \(C_ 2\). (English) Zbl 1051.39021 J. Phys. A, Math. Gen. 34, No. 26, 5389-5401 (2001). MSC: 39A70 17B37 33D80 37K30 81R12 81R50 PDFBibTeX XMLCite \textit{T. Kikuchi}, J. Phys. A, Math. Gen. 34, No. 26, 5389--5401 (2001; Zbl 1051.39021) Full Text: DOI arXiv
Ghose Choudhury, A.; Roy Chowdhury, A. On Bäcklund transformations and boundary conditions associated with the quantum inverse problem for a discrete nonlinear integrable system and its connection to Baxter’s \(Q\)-operator. (English) Zbl 1136.82314 Adv. Theor. Math. Phys. 5, No. 4, 679-696 (2001). MSC: 82B20 37K35 37N20 39A12 81R12 81U40 PDFBibTeX XMLCite \textit{A. Ghose Choudhury} and \textit{A. Roy Chowdhury}, Adv. Theor. Math. Phys. 5, No. 4, 679--696 (2001; Zbl 1136.82314) Full Text: DOI arXiv
Komori, Yasushi Ruijsenaars’ commuting difference operators and invariant subspace spanned by theta functions. (English) Zbl 1013.39010 J. Math. Phys. 42, No. 9, 4503-4522 (2001). MSC: 39A70 39A12 81R10 17B37 17B81 14K25 PDFBibTeX XMLCite \textit{Y. Komori}, J. Math. Phys. 42, No. 9, 4503--4522 (2001; Zbl 1013.39010) Full Text: DOI
Pirozerski, A. L.; Semenov-Tian-Shansky, M. A. \(Q\)-pseudodifference universal Drinfeld-Sokolov reduction. (English) Zbl 0994.37038 Uraltseva, N. N. (ed.), Proceedings of the St. Petersburg Mathematical Society. Vol. VII. Transl. from the Russian by Tamara Rozhkovskaya. Providence, RI: American Mathematical Society (AMS). Transl., Ser. 2, Am. Math. Soc. 203, 169-199 (2001). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 37K30 39A13 81R50 37K10 17B80 PDFBibTeX XMLCite \textit{A. L. Pirozerski} and \textit{M. A. Semenov-Tian-Shansky}, Transl., Ser. 2, Am. Math. Soc. 203, 169--199 (2001; Zbl 0994.37038)
Orlov, A. Yu.; Scherbin, D. M. Multivariate hypergeometric functions as \(\tau\)-functions of Toda lattice and Kadomtsev-Petviashvili equation. (English) Zbl 0988.37091 Physica D 152-153, 51-65 (2001). Reviewer: Samir Musayev (Baku) MSC: 37K20 33D80 33C80 37K05 39A12 37K30 PDFBibTeX XMLCite \textit{A. Yu. Orlov} and \textit{D. M. Scherbin}, Physica D 152--153, 51--65 (2001; Zbl 0988.37091) Full Text: DOI arXiv
Rybin, Andrei; Timonen, Jussi; Varzugin, Gennadii; Bullough, Robin K. \(q\)-deformed solitons and quantum solitons of the Maxwell-Bloch lattice. (English) Zbl 0967.81077 J. Phys. A, Math. Gen. 34, No. 1, 157-164 (2001). MSC: 81V80 78A60 81R50 37K99 39A12 81R12 PDFBibTeX XMLCite \textit{A. Rybin} et al., J. Phys. A, Math. Gen. 34, No. 1, 157--164 (2001; Zbl 0967.81077) Full Text: DOI arXiv
Hernández Heredero, R.; Levi, D.; Winternitz, P. Symmetry preserving discretization of the Burgers equation. (English) Zbl 0963.35168 Levi, Decio (ed.) et al., SIDE III - Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16-22, 1998. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 25, 197-208 (2000). MSC: 35Q53 37K30 22E70 39A12 PDFBibTeX XMLCite \textit{R. Hernández Heredero} et al., in: SIDE III -- Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16--22, 1998. Providence, RI: American Mathematical Society (AMS). 197--208 (2000; Zbl 0963.35168)
Tarasov, V.; Varchenko, A. Difference equations compatible with trigonometric KZ differential equations. (English) Zbl 0971.39009 Int. Math. Res. Not. 2000, No. 15, 801-829 (2000). Reviewer: Victor I.Tkachenko (Kyïv) MSC: 39A12 39A10 81R10 32G34 17B37 17B20 PDFBibTeX XMLCite \textit{V. Tarasov} and \textit{A. Varchenko}, Int. Math. Res. Not. 2000, No. 15, 801--829 (2000; Zbl 0971.39009) Full Text: DOI arXiv
Semenov-Tian-Shansky, M. A.; Sevostyanov, A. V. Drinfeld-Sokolov reduction for difference operators and deformations of \(W\)-algebras. II: The general semisimple case. (English) Zbl 0916.17021 Commun. Math. Phys. 192, No. 3, 631-647 (1998). Reviewer: Volodymyr Mazorchuk (Kyiv) MSC: 17B68 39A70 81R10 17B37 37J99 PDFBibTeX XMLCite \textit{M. A. Semenov-Tian-Shansky} and \textit{A. V. Sevostyanov}, Commun. Math. Phys. 192, No. 3, 631--647 (1998; Zbl 0916.17021) Full Text: DOI arXiv
Tsuboi, Zengo Analytic Bethe ansatz and functional equations for Lie superalgebra \(sl(r+1 |s+1)\). (English) Zbl 0940.81025 J. Phys. A, Math. Gen. 30, No. 22, 7975-7991 (1997). MSC: 81R10 82B23 39A10 PDFBibTeX XMLCite \textit{Z. Tsuboi}, J. Phys. A, Math. Gen. 30, No. 22, 7975--7991 (1997; Zbl 0940.81025) Full Text: DOI arXiv
Chau, Ling-Lie; Yamanaka, Itaru The KZ equation and the quantum-group difference equation in quantum self-dual Yang-Mills theory. (English) Zbl 0869.39002 J. Math. Phys. 37, No. 8, 3704-3712 (1996). MSC: 39A10 81R10 17B81 81T13 PDFBibTeX XMLCite \textit{L.-L. Chau} and \textit{I. Yamanaka}, J. Math. Phys. 37, No. 8, 3704--3712 (1996; Zbl 0869.39002) Full Text: DOI arXiv
Turbiner, Alexander; Post, Gerhard Operator identities, representations of algebras and the problem of normal ordering. (English) Zbl 0829.39001 J. Phys. A, Math. Gen. 27, No. 2, L9-L13 (1994). MSC: 39A10 47B39 17A70 81R50 17B37 81R10 PDFBibTeX XMLCite \textit{A. Turbiner} and \textit{G. Post}, J. Phys. A, Math. Gen. 27, No. 2, L\, 9-L\, 13 (1994; Zbl 0829.39001) Full Text: DOI arXiv
Ecalle, Jean Théorie itérative: Introduction à la théorie des invariants holomorphes. (French) Zbl 0285.26010 J. Math. pur. appl., IX. Sér. 54, 183-258 (1975). MSC: 26A18 13J05 22E65 39B05 PDFBibTeX XMLCite \textit{J. Ecalle}, J. Math. Pures Appl. (9) 54, 183--258 (1975; Zbl 0285.26010)