Symmetric crystals and affine Hecke algebras of type B

Details Symmetric crystals and affine Hecke algebras of type B Symmetric crystals and affine Hecke algebras of type B

2006-08-03

arxiv.org/abs/math/0608079v3

Proc. Japan Acad. 82, Ser. A (2006) 131--136

Mathematics

Representation Theory

Announcement paper, 9 pages

Scientific paper

The Lascoux-Leclerc-Thibon conjecture, reformulated and solved by S. Ariki, 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 the Lie algebra $gl_\infty$ or the affine Lie algebra $A^{(1)}_\ell$, and the irreducible representations correspond to the upper global bases. In this note, we formulate analogous conjectures for certain classes of irreducible representations of affine Hecke algebras of type B. We corrected typos.

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