Abstract
In a series of papers with S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, we developed two uniform combinatorial models 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 $t=0$. I will present our latest work, on the extension of the above results corresponding to the non-symmetric Macdonald polynomials. I will then explain the connection of this work to the $q$-Whittaker functions of Braverman-Finkelberg and their results, which extend to quantum $K$-theory Schubert calculus. Other related developments will also be mentioned.
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