Knuth relations, tableaux and MV-cycles
Representation Theory
2012-10-05 v1
Abstract
We give a geometric interpretation of the Knuth equivalence relations in terms of the affine Gra{\ss} mann variety. The Young tableaux are seen as sequences of coweights, called galleries. We show that to any gallery corresponds a Mirkovi\'c-Vilonen cycle and that two galleries are equivalent if, and only if, their associated MV cycles are equal. Words are naturally identified to some galleries. So, as a corollary, we obtain that two words are Knuth equivalent if, and only if, their associated MV cycles are equal.
Cite
@article{arxiv.1210.1308,
title = {Knuth relations, tableaux and MV-cycles},
author = {Stéphane Gaussent and Peter Littelmann and An Hoa Nguyen},
journal= {arXiv preprint arXiv:1210.1308},
year = {2012}
}