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Algebra Seminar

"Kirillov-Reshetikhin modules and Macdonald polynomials: a survey and applications "

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Date & time: Wednesday, 05 April 2017 at 2:00PM -

 

Christian Lenart, Albany, SUNY

"Kirillov-Reshetikhin modules and Macdonald polynomials: a survey and applications "

Time: 2:00 PM
Location: Hill 705
Abstract: This talk is largely self-contained.

In a series of papers with S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, we developed a uniform combinatorial model for (tensor products of one-column) Kirillov-Reshetikhin (KR) modules of affine Lie algebras. We also showed that their graded characters coincide with the specialization of symmetric Macdonald polynomials at t=0, and extended this result to non-symmetric Macdonald polynomials. I will present a survey of this work and of the recent applications, which include: computations related to KR crystals, crystal bases of level 0 extremal weight modules, Weyl modules (local, global, and generalized), q-Whittaker functions, and the quantum K-theory of flag varieties.

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Department of Mathematics

Department of Mathematics
Rutgers University
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