Mirkovi\'c-Vilonen basis in type A_1
Representation Theory
2020-09-04 v1
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 Mirkovi\'c-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.
Cite
@article{arxiv.2009.01278,
title = {Mirkovi\'c-Vilonen basis in type A_1},
author = {Pierre Baumann and Arnaud Demarais},
journal= {arXiv preprint arXiv:2009.01278},
year = {2020}
}
Comments
31 pages