Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function
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 Kir...
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| Format: | Article |
| Language: | en_US |
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Electronic Journal of Combinatorics
2014
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| Online Access: | http://hdl.handle.net/1721.1/89813 |
| _version_ | 1811069206747152384 |
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| author | Schilling, Anne Tingley, Peter |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Schilling, Anne Tingley, Peter |
| author_sort | Schilling, Anne |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:07:24Z |
| format | Article |
| id | mit-1721.1/89813 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:07:24Z |
| publishDate | 2014 |
| publisher | Electronic Journal of Combinatorics |
| record_format | dspace |
| spelling | mit-1721.1/898132022-09-23T11:01:23Z Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function Schilling, Anne Tingley, Peter Massachusetts Institute of Technology. Department of Mathematics Tingley, Peter 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. National Science Foundation (U.S.) (Grant DMS-0902649) 2014-09-18T17:15:52Z 2014-09-18T17:15:52Z 2012-04 2011-10 Article http://purl.org/eprint/type/JournalArticle 1077-8926 http://hdl.handle.net/1721.1/89813 Schilling, Anne, and Peter Tingley. "Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function." Electronic Journal of Combinatorics, Volume 19, Issue 2 (2012). en_US http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i2p4 Electronic Journal of Combinatorics 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. application/pdf Electronic Journal of Combinatorics Electronic Journal of Combinatorics |
| spellingShingle | Schilling, Anne Tingley, Peter Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function |
| title | Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function |
| title_full | Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function |
| title_fullStr | Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function |
| title_full_unstemmed | Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function |
| title_short | Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function |
| title_sort | demazure crystals kirillov reshetikhin crystals and the energy function |
| url | http://hdl.handle.net/1721.1/89813 |
| work_keys_str_mv | AT schillinganne demazurecrystalskirillovreshetikhincrystalsandtheenergyfunction AT tingleypeter demazurecrystalskirillovreshetikhincrystalsandtheenergyfunction |