English

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.

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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

R2 v1 2026-06-23T18:16:38.870Z