Mirković-Vilonen basis in type A₁

2020/09/02 by Baumann, Pierre, Demarais, Arnaud
#22E46 (Primary) 14M15 (Secondary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2009.01278

Abstract

Let G be a reductive connected algebraic group over the field of complex numbers. Through the geometric Satake equivalence, the fundamental classes of the Mirković-Vilonen cycles define a basis in each tensor product of rational irreducible representations of G. In the case G=SL₂(C), we show that this basis coincides with the dual canonical basis at q=1.

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• On Mirković-Vilonen cycles and crystals combinatorics
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• Mirkovic-Vilonen cycles and polytopes