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2014 | 12 | 5 | 694-710
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Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a $$\mathfrak{g}\mathfrak{l}_n$$ partial flag variety. These hypergeometric solutions manifest the Landau-Ginzburg mirror symmetry for the cotangent bundle of a partial flag variety.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
5
Strony
694-710
Opis fizyczny
Daty
wydano
2014-05-01
online
2014-02-15
Twórcy
Bibliografia
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  • [5] Givental A.B., Gromov-Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J., 2001, 1(4), 551–568
  • [6] Gorbounov V., Rimányi R., Tarasov V., Varchenko A., Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra, J. Geom. Phys., 2013, 74, 56–86 http://dx.doi.org/10.1016/j.geomphys.2013.07.006
  • [7] Markov Y., Varchenko A., Hypergeometric solutions of trigonometric KZ equations satisfy dynamical difference equations, Adv. Math., 2002, 166(1), 100–147 http://dx.doi.org/10.1006/aima.2001.2027
  • [8] Maulik D., Okounkov A., Quantum groups and quantum cohomology, preprint available at http://arxiv.org/abs/1211.1287
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  • [10] Mukhin E., Tarasov V., Varchenko A., Bethe algebra of the \(\mathfrak{g}\mathfrak{l}_{N + 1}\) Gaudin model and algebra of functions on the critical set of the master function, In: New Trends in Quantum Integrable Systems, World Scientific, Hackensack, 2011, 307–324 http://dx.doi.org/10.1142/9789814324373_0016
  • [11] Mukhin E., Tarasov V., Varchenko A., Three sides of the geometric Langlands correspondence for \(\mathfrak{g}\mathfrak{l}_N\) Gaudin model and Bethe vector averaging maps, In: Arrangements of Hyperplanes-Sapporo 2009, Sapporo, August 1–13, 2009, Adv. Stud. Pure Math., 62, Mathematrical Society of Japan, Tokyo, 2012, 475–511
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  • [14] Rimányi R., Stevens L., Varchenko A., Combinatorics of rational functions and Poincaré-Birchoff-Witt expansions of the canonical \(U(\mathfrak{n}\_)\) -valued differential form, Ann. Comb., 2005, 9(1), 57–74 http://dx.doi.org/10.1007/s00026-005-0241-3
  • [15] Rimányi R., Tarasov V., Varchenko A., Partial flag varieties, stable envelopes and weight functions, Quantum Topol. (in press), preprint available at http://arxiv.org/abs/1212.6240
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  • [17] Tarasov V., Varchenko A., Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math., 1997, 128(3), 501–588 http://dx.doi.org/10.1007/s002220050151
  • [18] Tarasov V., Varchenko A., Difference equations compatible with trigonometric KZ differential equations, Internat. Math. Res. Notices, 2000, 15, 801–829 http://dx.doi.org/10.1155/S1073792800000441
  • [19] Tarasov V., Varchenko A., Duality for Knizhnik-Zamolodchikov and dynamical equations, Acta Appl. Math., 2002, 73(1–2), 141–154 http://dx.doi.org/10.1023/A:1019787006990
  • [20] Tarasov V., Varchenko A., Combinatorial formulae for nested Bethe vectors, SIGMA Symmetry Integrability Geom. Methods Appl., 2013, 9, #048
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Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0376-8
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