Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function
Name
Schilling-2012-Demazure crystals.pdf
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492.31 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Schilling, Anne
Tingley, Peter
Date Issued
April 2012
Journal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Schilling, Anne, and Peter Tingley. "Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function." Electronic Journal of Combinatorics, Volume 19, Issue 2 (2012).
Version
Final published version
Abstract
It has previously been shown that, at least for non-exceptional Kac-Moody Lie algebras, there is a close connection between Demazure crystals and tensor products of Kirillov-Reshetikhin crystals. In particular, certain Demazure crystals are isomorphic as classical crystals to tensor products of Kirillov-Reshetikhin crystals via a canonically chosen isomorphism. Here we show that this isomorphism intertwines the natural affine grading on Demazure crystals with a combinatorially defined energy function. As a consequence, we obtain a formula of the Demazure character in terms of the energy function, which has applications to Macdonald polynomials and q-deformed Whittaker functions.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.37236/2184
