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Genus Two analogue of A_1 spherical DAHA

Le : 06/12/2017 10h45
Par : Semeon Artamonov (Rutgers)
Lieu : I001
Lien web :
Résumé : In my talk I will consider a quantum integrable system with two generic complex parameters q,t whose classical phase space is the moduli space of flat SL(2,C) connections on a genus two surface. This system and its eigenfunctions provide genus two generalizations of the trigonometric Ruijsenaars-Schneider model and Macdonald polynomials, respectively. I will show that the Mapping Class Group of a genus two surface acts by automorphisms of the algebra of operators of this system. Therefore this algebra can be viewed as a genus two generalization of A_1 spherical DAHA. (based on arXiv:1704.02947 joint with Sh. Shakirov)