Kac, Victor; van de Leur, Johan Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras. (English) Zbl 1521.37073 J. Math. Phys. 64, No. 9, Article ID 091702, 91 p. (2023). MSC: 37K10 37K30 17B67 17B80 PDFBibTeX XMLCite \textit{V. Kac} and \textit{J. van de Leur}, J. Math. Phys. 64, No. 9, Article ID 091702, 91 p. (2023; Zbl 1521.37073) Full Text: DOI arXiv
Kac, Victor; van de Leur, Johan The generalized Giambelli formula and polynomial KP and CKP tau-functions. (English) Zbl 1517.37071 J. Phys. A, Math. Theor. 56, No. 18, Article ID 185203, 28 p. (2023). MSC: 37K20 37K10 PDFBibTeX XMLCite \textit{V. Kac} and \textit{J. van de Leur}, J. Phys. A, Math. Theor. 56, No. 18, Article ID 185203, 28 p. (2023; Zbl 1517.37071) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele On Lax operators. (English) Zbl 1522.37077 Jpn. J. Math. (3) 17, No. 1, 63-116 (2022). MSC: 37K10 37K06 37K20 37K30 17B80 PDFBibTeX XMLCite \textit{A. De Sole} et al., Jpn. J. Math. (3) 17, No. 1, 63--116 (2022; Zbl 1522.37077) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele Adler-Oevel-Ragnisco type operators and Poisson vertex algebras. arXiv:2208.00154 Preprint, arXiv:2208.00154 [nlin.SI] (2022). MSC: 17B69 37K10 37K30 BibTeX Cite \textit{A. De Sole} et al., ``Adler-Oevel-Ragnisco type operators and Poisson vertex algebras'', Preprint, arXiv:2208.00154 [nlin.SI] (2022) Full Text: arXiv OA License
Kac, Victor G.; Rozhkovskaya, Natasha; van de Leur, Johan Polynomial tau-functions of the KP, BKP, and the \(s\)-component KP hierarchies. (English) Zbl 1464.37073 J. Math. Phys. 62, No. 2, Article ID 021702, 25 p. (2021). MSC: 37K10 37K20 PDFBibTeX XMLCite \textit{V. G. Kac} et al., J. Math. Phys. 62, No. 2, Article ID 021702, 25 p. (2021; Zbl 1464.37073) Full Text: DOI arXiv
Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; van de Leur, Johan \( \underline{p} \)-reduced multicomponent KP hierarchy and classical \(\mathcal{W} \)-algebras \(\mathcal{W}(\mathfrak{gl}_N,\underline{p})\). (English) Zbl 1458.37068 Commun. Math. Phys. 380, No. 2, 655-722 (2020). MSC: 37K10 37K30 17B63 17B69 17B80 PDFBibTeX XMLCite \textit{S. Carpentier} et al., Commun. Math. Phys. 380, No. 2, 655--722 (2020; Zbl 1458.37068) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; Wakimoto, Minoru Poisson \(\lambda\)-brackets for differential-difference equations. (English) Zbl 1473.37079 Int. Math. Res. Not. 2020, No. 13, 4144-4190 (2020). Reviewer: Yarema Prykarpatskyy (Kraków) MSC: 37K06 37K30 37J06 37J37 39A36 17B63 PDFBibTeX XMLCite \textit{A. De Sole} et al., Int. Math. Res. Not. 2020, No. 13, 4144--4190 (2020; Zbl 1473.37079) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; Wakimoto, Minoru Local and non-local multiplicative Poisson vertex algebras and differential-difference equations. (English) Zbl 1421.35323 Commun. Math. Phys. 370, No. 3, 1019-1068 (2019). MSC: 35Q53 37K10 17B80 17B69 37K30 PDFBibTeX XMLCite \textit{A. De Sole} et al., Commun. Math. Phys. 370, No. 3, 1019--1068 (2019; Zbl 1421.35323) Full Text: DOI arXiv Link
Kac, Victor; Van De Leur, Johan Polynomial tau-functions of BKP and DKP hierarchies. (English) Zbl 1421.37028 J. Math. Phys. 60, No. 7, 071702, 10 p. (2019). Reviewer: Ahmed Lesfari (El Jadida) MSC: 37K10 35Q53 20C25 37K30 PDFBibTeX XMLCite \textit{V. Kac} and \textit{J. Van De Leur}, J. Math. Phys. 60, No. 7, 071702, 10 p. (2019; Zbl 1421.37028) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele Classical affine \(\mathcal W\)-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras. (English) Zbl 1426.17015 Commun. Math. Phys. 360, No. 3, 851-918 (2018). MSC: 17B80 17B69 37K10 37K30 PDFBibTeX XMLCite \textit{A. De Sole} et al., Commun. Math. Phys. 360, No. 3, 851--918 (2018; Zbl 1426.17015) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele A new scheme of integrability for (bi)Hamiltonian PDE. (English) Zbl 1393.17048 Commun. Math. Phys. 347, No. 2, 449-488 (2016). MSC: 17B80 17B63 17B69 37K30 PDFBibTeX XMLCite \textit{A. De Sole} et al., Commun. Math. Phys. 347, No. 2, 449--488 (2016; Zbl 1393.17048) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele Classical affine \(\mathcal{W}\)-algebras for \(\mathfrak{gl}_N\) and associated integrable Hamiltonian hierarchies. (English) Zbl 1433.17038 Commun. Math. Phys. 348, No. 1, 265-319 (2016). MSC: 17B80 17B69 37K10 37K30 PDFBibTeX XMLCite \textit{A. De Sole} et al., Commun. Math. Phys. 348, No. 1, 265--319 (2016; Zbl 1433.17038) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele Structure of classical (finite and affine) \(\mathcal W\)-algebras. (English) Zbl 1395.17063 J. Eur. Math. Soc. (JEMS) 18, No. 9, 1873-1908 (2016). MSC: 17B69 17B08 17B63 37K30 PDFBibTeX XMLCite \textit{A. De Sole} et al., J. Eur. Math. Soc. (JEMS) 18, No. 9, 1873--1908 (2016; Zbl 1395.17063) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Turhan, Refik On integrability of some bi-Hamiltonian two field systems of partial differential equations. (English) Zbl 1321.37068 J. Math. Phys. 56, No. 5, 051503, 20 p. (2015). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37K10 37K20 14H60 14H70 53D17 17B63 PDFBibTeX XMLCite \textit{A. De Sole} et al., J. Math. Phys. 56, No. 5, 051503, 20 p. (2015; Zbl 1321.37068) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele Integrability of Dirac reduced bi-Hamiltonian equations. (English) Zbl 1326.35310 Ancona, Vincenzo (ed.) et al., Trends in contemporary mathematics. Selected talks based on the presentations at the INdAM day, June 18, 2014. Cham: Springer (ISBN 978-3-319-05253-3/hbk; 978-3-319-05254-0/ebook). Springer INdAM Series 8, 13-32 (2014). MSC: 35Q53 17B80 37K10 37K30 17B63 PDFBibTeX XMLCite \textit{A. De Sole} et al., Springer INdAM Ser. 8, 13--32 (2014; Zbl 1326.35310) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Turhan, Refik A new approach to the Lenard-Magri scheme of integrability. (English) Zbl 1305.37035 Commun. Math. Phys. 330, No. 1, 107-122 (2014). Reviewer: Mohamed Selmi (Sousse-Riadh) MSC: 37K10 37K30 17B63 17B70 17B80 PDFBibTeX XMLCite \textit{A. De Sole} et al., Commun. Math. Phys. 330, No. 1, 107--122 (2014; Zbl 1305.37035) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. (English) Zbl 1320.37031 Commun. Math. Phys. 323, No. 2, 663-711 (2013). MSC: 37K10 37K30 17B80 17B68 PDFBibTeX XMLCite \textit{A. De Sole} et al., Commun. Math. Phys. 323, No. 2, 663--711 (2013; Zbl 1320.37031) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G. Non-local Poisson structures and applications to the theory of integrable systems. (English) Zbl 1286.37062 Jpn. J. Math. (3) 8, No. 2, 233-347 (2013). Reviewer: Mohamed Selmi (Sousse-Riadh) MSC: 37K10 35Q53 17B69 37K30 17B63 PDFBibTeX XMLCite \textit{A. De Sole} and \textit{V. G. Kac}, Jpn. J. Math. (3) 8, No. 2, 233--347 (2013; Zbl 1286.37062) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G. The variational Poisson cohomology. (English) Zbl 1290.17027 Jpn. J. Math. (3) 8, No. 1, 1-145 (2013). Reviewer: Nenad Manojlović (Faro) MSC: 17B80 37K10 17B69 37K30 17B56 PDFBibTeX XMLCite \textit{A. De Sole} and \textit{V. G. Kac}, Jpn. J. Math. (3) 8, No. 1, 1--145 (2013; Zbl 1290.17027) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G. Essential variational Poisson cohomology. (English) Zbl 1297.17012 Commun. Math. Phys. 313, No. 3, 837-864 (2012). MSC: 17B80 37K30 17B56 17B70 PDFBibTeX XMLCite \textit{A. De Sole} and \textit{V. G. Kac}, Commun. Math. Phys. 313, No. 3, 837--864 (2012; Zbl 1297.17012) Full Text: DOI arXiv
De Sole, Alberto; Kac, Victor G. Non-local Poisson structures and applications to the theory of integrable systems II. arXiv:1211.2391 Preprint, arXiv:1211.2391 [math-ph] (2012). MSC: 37K10 35Q53 17B80 17B69 37K30 17B63 BibTeX Cite \textit{A. De Sole} and \textit{V. G. Kac}, ``Non-local Poisson structures and applications to the theory of integrable systems II'', Preprint, arXiv:1211.2391 [math-ph] (2012) Full Text: arXiv OA License
De Sole, Alberto; Kac, Victor G. Non-local Hamiltonian structures and applications to the theory of integrable systems I. arXiv:1210.1688 Preprint, arXiv:1210.1688 [math-ph] (2012). MSC: 37K10 35Q53 17B80 17B69 37K30 17B63 BibTeX Cite \textit{A. De Sole} and \textit{V. G. Kac}, ``Non-local Hamiltonian structures and applications to the theory of integrable systems I'', Preprint, arXiv:1210.1688 [math-ph] (2012) Full Text: arXiv OA License
Barakat, Aliaa; De Sole, Alberto; Kac, Victor G. Poisson vertex algebras in the theory of Hamiltonian equations. (English) Zbl 1244.17017 Jpn. J. Math. (3) 4, No. 2, 141-252 (2009). MSC: 17B80 37K10 17B69 37K30 PDFBibTeX XMLCite \textit{A. Barakat} et al., Jpn. J. Math. (3) 4, No. 2, 141--252 (2009; Zbl 1244.17017) 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 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, V. G.; Raina, A. K. Bombay lectures on highest weight representations of infinite dimensional Lie algebras. (English) Zbl 0668.17012 Advanced Series in Mathematical Physics, Vol. 2. Singapore-New Jersey-Hong Kong: World Scientific, ix, 145 p. (1987). Reviewer: Shrawan Kumar (Bombay) MSC: 17B65 17B67 17B68 37K10 37K30 37K40 17-02 17B10 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. 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