Knuth relations, tableaux and MV-cyclesReport as inadecuate




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1 ICJ - Institut Camille Jordan Villeurbanne 2 Géométrie IECL - Institut Élie Cartan de Lorraine 3 Mathematisches Institut, Universität zu Köln

Abstract : We give a geometric interpretation of the Knuth equivalence relations in terms of the affine Graß mann variety. The Young tableaux are seen as sequences of coweights, called galleries. We show that to any gallery corresponds a Mirković-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.





Author: Stéphane Gaussent - Peter Littelmann - An Hoa Nguyen -

Source: https://hal.archives-ouvertes.fr/



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