dorsal/arxiv
View SchemaCrystal Graphs and $q$-Analogues of Weight Multiplicities for the Root System $A_n$
| Authors | A. Lascoux, B. Leclerc, J. -Y. Thibon |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9503001 |
| URL | https://arxiv.org/abs/q-alg/9503001 |
| DOI | 10.1007/BF00750843 |
Abstract
We give an expression of the $q$-analogues of the multiplicities of weights in irreducible $\sl_{n+1}$-modules in terms of the geometry of the crystal graph attached to the corresponding $U_q(\sl_{n+1})$-modules. As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight, refining Kostant's generalized exponents.
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"abstract": "We give an expression of the $q$-analogues of the multiplicities of weights\nin irreducible $\\sl_{n+1}$-modules in terms of the geometry of the crystal\ngraph attached to the corresponding $U_q(\\sl_{n+1})$-modules. As an\napplication, we describe multivariate polynomial analogues of the\nmultiplicities of the zero weight, refining Kostant\u0027s generalized exponents.",
"arxiv_id": "q-alg/9503001",
"authors": [
"A. Lascoux",
"B. Leclerc",
"J. -Y. Thibon"
],
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"q-alg",
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"doi": "10.1007/BF00750843",
"title": "Crystal Graphs and $q$-Analogues of Weight Multiplicities for the Root System $A_n$",
"url": "https://arxiv.org/abs/q-alg/9503001"
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