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Standard Young Tableaux in the Weyl Group Setting

✍ Scribed by Jozsef Losonczy

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 70 KB
Volume: 220
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7931

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✦ Synopsis

A generalization of the notion of standard Young tableau has recently arisen from work on the representation theory of affine Hecke algebras. In the generalized setting, a standard tableau is defined to be any element of a finite Weyl group whose inversion set satisfies a certain pair of intersection conditions. In this paper, we prove that the set of generalized standard tableaux of fixed shape, when nonempty, is a certain interval in the weak ordering. In addition, we establish a nonemptiness criterion for the set of standard tableaux of prescribed shape. These results are obtained for shapes that satisfy an integrality condition. ᮊ 1999 Aca- demic Press

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