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Demazure modules and graded limits of minimal affinizations


Author: Katsuyuki Naoi
Journal: Represent. Theory 17 (2013), 524-556
MSC (2010): Primary 17B10, 17B37; Secondary 20G42
DOI: https://doi.org/10.1090/S1088-4165-2013-00442-9
Published electronically: October 28, 2013
MathSciNet review: 3120578
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Abstract: For a minimal affinization over a quantum loop algebra of type $ BC$, we provide a character formula in terms of Demazure operators and multiplicities in terms of crystal bases. We also prove the formula for the limit of characters conjectured by Mukhin and Young. These are achieved by verifying that its graded limit (a variant of a classical limit) is isomorphic to some multiple generalization of a Demazure module, and by determining the defining relations of the graded limit.


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Additional Information

Katsuyuki Naoi
Affiliation: University of Tokyo, Kavli Institute for the Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa, 277-8583 Japan
Email: katsuyuki.naoi@ipmu.jp

DOI: https://doi.org/10.1090/S1088-4165-2013-00442-9
Received by editor(s): October 5, 2012
Received by editor(s) in revised form: May 12, 2013, and June 17, 2013
Published electronically: October 28, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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