Cauchy Identities for Genus Two Schur Polynomials
演讲者
Semeon Arthamonov
时间
2025年10月24日 13:00 至 14:30
地点
A3-4-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
In joint work with Shamil Shakirov, we introduced a genus two analogue of Macdonald polynomials. These polynomials form a system of common eigenfunctions for a family of q-difference operators that generalize the A_1-type Macdonald operators. We demonstrated that the algebra generated by these operators together with multiplication operators admits an action of the genus two mapping class group by automorphisms. This generalizes the well-known action of SL(2, Z) on the spherical Double Affine Hecke Algebra.
In this talk, I will present follow-up work in which we derive Cauchy identities for a specialization of our polynomials—specifically, for the genus two Schur polynomials (the t=q=1 case). This work is based on arXiv:2506.18338, joint with Sh. Shakirov and W. Yan.
In this talk, I will present follow-up work in which we derive Cauchy identities for a specialization of our polynomials—specifically, for the genus two Schur polynomials (the t=q=1 case). This work is based on arXiv:2506.18338, joint with Sh. Shakirov and W. Yan.