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CRYSTAL GRAPHS AND Q-ANALOGS OF WEIGHT MULTIPLICITIES FOR THE ROOT-SYSTEM A(N)

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 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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https://hal-upec-upem.archives-ouvertes.fr/hal-00693520
Contributor : Alain Lascoux <>
Submitted on : Wednesday, May 2, 2012 - 5:41:00 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:06 PM

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Alain Lascoux, B Leclerq, Jean-Yves Thibon. CRYSTAL GRAPHS AND Q-ANALOGS OF WEIGHT MULTIPLICITIES FOR THE ROOT-SYSTEM A(N). Letters in Mathematical Physics, Springer Verlag, 1995, 35 (4), pp.359--374. ⟨10.1007/BF00750843⟩. ⟨hal-00693520⟩

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