Components of V(ρ)⊗ V(ρ)

2015/08/12 by Shrawan Kumar, Kumar, Shrawan
Mathematics · #14C17 #14L30 #14N15 #14N35 #20G05 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:14C17 #msc:14L30 #msc:14N15 #msc:14N35 #msc:20G05

paper · pdf · doi:10.48550/arxiv.1508.03071

7 pages

arxiv created 2015/08/12 · arxiv updated 2015/08/14

Abstract

Kostant asked the following question: Let \mathfrakg be a simple Lie algebra over the complex numbers. Let λ be a dominant integral weight. Then, V(λ) is a component of V(ρ)⊗ V(ρ) if and only if λ≤ 2ρ under the usual Bruhat-Chevalley order on the set of weights. We give an affirmative answer to this question up to a saturation factor. In particular, the question is answered affirmatively for the special linear Lie algebras due to the Saturation Theorem of Knutson-Tao.

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