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

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

1995-03-04

arxiv.org/abs/q-alg/9503001v1

Mathematics

Quantum Algebra

LaTeX file with epic, eepic pictures, 17 pages, November 1994, to appear in Lett. Math. Phys

Scientific paper

10.1007/BF00750843

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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