Simplified presentations and embeddings of Demazure modules

Kus, D and Venkatesh, R (2024) Simplified presentations and embeddings of Demazure modules. In: Israel Journal of Mathematics .

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Abstract

For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g., level one in type A) which becomes in the limit (for anti-dominant weights) the well-known embedding of finite-dimensional irreducible modules of the underlying simple Lie algebra into the tensor product of fundamental modules. To achieve this goal, we first simplify the presentation of these modules extending the results of 13 in the g-stable case. As an application, we propose a crystal theoretic way to find classical decompositions with respect to a maximal semi-simple Lie subalgebra by identifying the Demazure crystal as a connected component in the corresponding tensor product of crystals. © The Hebrew University of Jerusalem 2024.

Item Type:	Journal Article
Publication:	Israel Journal of Mathematics
Publisher:	Hebrew University Magnes Press
Additional Information:	The copyright for this article belongs to Hebrew University Magnes Press.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	06 Sep 2024 05:30
Last Modified:	06 Sep 2024 05:30
URI:	http://eprints.iisc.ac.in/id/eprint/85974

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