Brito, M and Chari, V and Kus, D and Venkatesh, R (2022) Quantum Affine Algebras, Graded Limits and Flags. In: Journal of the Indian Institute of Science .
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Abstract
In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations of these algebras. This connection arises via the notion of the graded and classical limit of finite-dimensional representations of quantum affine algebras. We explain how this study has led to interesting connections with Macdonald polynomials and discuss a BGG-type reciprocity result. We also discuss the role of Demazure modules in this theory and several recent results on the presentation, structure and combinatorics of Demazure modules.
| Item Type: | Journal Article |
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| Publication: | Journal of the Indian Institute of Science |
| Publisher: | Springer |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | 'current; Classical limits; Combinatorics; Dimensional representation; Finite dimensional; Macdonald polynomials; Representation theory, Algebra |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 04 Aug 2022 11:01 |
| Last Modified: | 04 Aug 2022 11:01 |
| URI: | https://eprints.iisc.ac.in/id/eprint/75335 |
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