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July 2007 Crystals and affine Hecke algebras of type D
Masaki Kashiwara, Vanessa Miemietz
Proc. Japan Acad. Ser. A Math. Sci. 83(7): 135-139 (July 2007). DOI: 10.3792/pjaa.83.135

Abstract

The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra $\mathfrak{g}$ where $\mathfrak{g}$ is $\mathfrak{gl}_{\infty}$ or the affine Lie algebra $A^{(1)}_{\ell}$, and the irreducible representations correspond to the upper global bases. Recently, N. Enomoto and the first author presented the notion of symmetric crystals and formulated analogous conjectures for the affine Hecke algebras of type B. In this note, we present similar conjectures for certain classes of irreducible representations of affine Hecke algebras of type D. The crystal for type D is a double cover of the one for type B.

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Masaki Kashiwara. Vanessa Miemietz. "Crystals and affine Hecke algebras of type D." Proc. Japan Acad. Ser. A Math. Sci. 83 (7) 135 - 139, July 2007. https://doi.org/10.3792/pjaa.83.135

Information

Published: July 2007
First available in Project Euclid: 18 January 2008

zbMATH: 1206.17014
MathSciNet: MR2361426
Digital Object Identifier: 10.3792/pjaa.83.135

Subjects:
Primary: 17B37, 20C08
Secondary: 20G05

Rights: Copyright © 2007 The Japan Academy

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Vol.83 • No. 7 • July 2007
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