Document Type

Article

Publication Date

2012

Publication Title

Electronic Journal of Combinatorics

Volume

19

Issue

2

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.

Comments

Author Posting. © Schilling and Tingley, 2012. This article is posted here by permission of the authors for personal use, not for redistribution. The article was published in the Electronic Journal of Combinatorics, Volume 19, Issue 2, 2012. http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i2p4

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Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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