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arXiv · 1210.1308

Knuth relations, tableaux and MV-cycles

Stéphane Gaussent·Peter Littelmann·An Hoa Nguyen
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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.

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BibTeXRIS

Stéphane Gaussent, Peter Littelmann, An Hoa Nguyen. 2012-10-04. Knuth relations, tableaux and MV-cycles. https://arxiv.org/abs/1210.1308

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