PIRSA:17040051

Traces of intertwiners for quantum affine sl_2, affine Macdonald conjectures, and Felder-Varchenko functions

Sun, Y. (2017). Traces of intertwiners for quantum affine sl_2, affine Macdonald conjectures, and Felder-Varchenko functions. Perimeter Institute. https://pirsa.org/17040051

Sun, Yi. Traces of intertwiners for quantum affine sl_2, affine Macdonald conjectures, and Felder-Varchenko functions. Perimeter Institute, Apr. 24, 2017, https://pirsa.org/17040051 

          @misc{ pirsa_PIRSA:17040051,
            doi = {10.48660/17040051},
            url = {https://pirsa.org/17040051},
            author = {Sun, Yi},
            keywords = {Mathematical physics},
            language = {en},
            title = {Traces of intertwiners for quantum affine sl_2, affine Macdonald conjectures, and Felder-Varchenko functions},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {apr},
            note = {PIRSA:17040051 see, \url{https://pirsa.org}}
          }

Yi Sun Columbia University

DOI 10.48660/17040051
Collection
Talk Type Scientific Series
Subject

Abstract

This talk concerns a family of special functions common to the study of quantum conformal blocks and hypergeometric solutions to q-KZB type equations.  In the first half, I will explain two methods for their construction -- as traces of intertwining operators between representations of quantum affine algebras and as certain theta hypergeometric integrals we term Felder-Varchenko functions.  I will then explain our proof by bosonization the first case of Etingof-Varchenko's conjecture that these constructions are related by a simple renormalization.

 

The second half of the talk will concern applications to affine Macdonald theory.  I will present refinements of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr.  I will then explain how to prove the first non-trivial cases of these conjectures by combining the methods of the first half and well-chosen applications of the elliptic beta integral.   The second half of this talk is joint work with E. Rains and A. Varchenko.