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arXiv · q-alg/9503001

Crystal Graphs and $q$-Analogues of Weight Multiplicities for the Root System $A_n$

A. Lascoux·B. Leclerc·J. -Y. Thibon
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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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BibTeXRIS

A. Lascoux, B. Leclerc, J. -Y. Thibon. 1995-03-04. Crystal Graphs and $q$-Analogues of Weight Multiplicities for the Root System $A_n$. https://doi.org/10.1007/bf00750843

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