Lusztig $q$-weight multiplicities and Kirillov-Reshetikhin crystals
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915122247630848 |
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| author | Choi, Hyeonjae Kim, Donghyun Lee, Seung Jin |
| author_facet | Choi, Hyeonjae Kim, Donghyun Lee, Seung Jin |
| contents | Lusztig $q$-weight multiplicities extend the Kostka-Foulkes polynomials to a broader range of Lie types. In this work, we investigate these multiplicities through the framework of Kirillov-Reshetikhin crystals. Specifically, for type $C$ with dominant weights and type $B$ with dominant spin weights, we present a combinatorial formula for Lusztig $q$-weight multiplicities in terms of energy functions of Kirillov-Reshetikhin crystals, generalizing the charge statistic on semistandard Young tableaux for type $A$. Additionally, we introduce level-restricted $q$-weight multiplicities for nonexceptional types, and prove positivity by providing their combinatorial formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lusztig $q$-weight multiplicities and Kirillov-Reshetikhin crystals Choi, Hyeonjae Kim, Donghyun Lee, Seung Jin Combinatorics Representation Theory Lusztig $q$-weight multiplicities extend the Kostka-Foulkes polynomials to a broader range of Lie types. In this work, we investigate these multiplicities through the framework of Kirillov-Reshetikhin crystals. Specifically, for type $C$ with dominant weights and type $B$ with dominant spin weights, we present a combinatorial formula for Lusztig $q$-weight multiplicities in terms of energy functions of Kirillov-Reshetikhin crystals, generalizing the charge statistic on semistandard Young tableaux for type $A$. Additionally, we introduce level-restricted $q$-weight multiplicities for nonexceptional types, and prove positivity by providing their combinatorial formulas. |
| title | Lusztig $q$-weight multiplicities and Kirillov-Reshetikhin crystals |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2412.20757 |