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New results on Kirillov-Reshetikhin modules and Macdonald polynomials Lenart, Cristian
Description
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.
Item Metadata
| Title |
New results on Kirillov-Reshetikhin modules and Macdonald polynomials
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-07-26T13:31
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| Description |
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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| Extent |
41 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: SUNY Albany
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| Series | |
| Date Available |
2017-02-05
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0340895
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International