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arXiv · 2009.01278

Mirković-Vilonen basis in type A_1

Pierre Baumann·Arnaud Demarais
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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=SL_2(C), we show that this basis coincides with the dual canonical basis at q=1.

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Pierre Baumann, Arnaud Demarais. 2020-09-02. Mirković-Vilonen basis in type A_1. https://arxiv.org/abs/2009.01278

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