Abstract
We give an expression of theq-analogues of the multiplicities of weights in irreducible\(\mathfrak{s}\mathfrak{l}_{n + 1} - modules\) in terms of the geometry of the crystal graph attached to corresponding\(U_q (\mathfrak{s}\mathfrak{l}_{n + 1} ) - modules\). As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight, refining Kostant's generalized exponents.
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Lascoux, A., Leclerc, B. & Thibon, JY. Crystal graphs andq-analogues of weight multiplicities for the root systemA n . Lett Math Phys 35, 359–374 (1995). https://doi.org/10.1007/BF00750843
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DOI: https://doi.org/10.1007/BF00750843