Seminars & Colloquia Calendar

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Lie Group Quantum Mathematics Seminar

"Affine Macdonald conjectures and special values of Felder-Varchenko functions"

Date & time: Friday, 07 April 2017 at 12:00PM -


Yi Sun, Columbia University

"Affine Macdonald conjectures and special values of Felder-Varchenko functions"

Time: 12:00 PM
Location: Hill 705
Abstract: I will explain how to refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr. and to prove the first non-trivial cases of these conjectures. Our method applies recent work of the speaker to relate these conjectures for U_q(sl_2 hat) to evaluations of certain theta hypergeometric integrals defined by Felder-Varchenko. We then evaluate the resulting integrals, which may be of independent interest, by well-chosen applications of the elliptic beta integral of Spiridonov.

These results are joint work with E. Rains and A. Varchenko.

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