Cluster realization of spherical DAHA

Abstract: Spherical subalgebra of Cherednik's double affine Hecke algebra of type A admits a polynomial representation in which its generators act via elementary symmetric functions and Macdonald operators. Recognizing the elementary symmetric functions as eigenfunctions of quantum Toda Hamiltonians, and applying (the inverse of) the Toda spectral transform, one obtains a new representation of spherical DAHA. In this talk, I will discuss how this new representation gives rise to an injective homomorphism from the spherical DAHA into a quantum cluster algebra in such a way that the action of the modular group on the former is realized via cluster transformations.

The talk is based on a joint work in progress with Philippe Di Francesco, Rinat Kedem, and Gus Schrader.

quantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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