Specialized Macdonald polynomials, quantum K-theory, and Kirillov-Reshetikhin modules
Event details
| Date | 03.03.2014 |
| Hour | 15:15 › 17:00 |
| Speaker | Cristian Lenart, Max-Planck-Institut, Bonn, and State University of New York at Albany |
| Location | |
| Category | Conferences - Seminars |
The (symmetric) Macdonald polynomials are Weyl group invariant polynomials with rational function coefficients in q,t, which specialize to the irreducible Lie algebra characters upon setting q=t=0. Quantum K-theory is a K-theoretic generalization of quantum cohomology. Kirillov-Reshetikhin (KR) modules are certain finite-dimensional modules for affine Lie algebras. Braverman and Finkelberg related the Macdonald polynomials specialized at t=0 to the quantum K-theory of flag varieties. With S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, I proved that the same specialization of Macdonald polynomials equals the graded character of a tensor product of (one-column) KR modules. I will discuss the combinatorics underlying these connections.
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