Symmetric Crystals and LLTA Type Conjectures for the Affine Hecke Algebras of Type B

Details Symmetric Crystals and LLTA Type Conjectures for the Affine Hecke Algebras of Type B Symmetric Crystals and LLTA Type Conjectures for the Affine Hecke Algebras of Type B

2007-05-27

arxiv.org/abs/0705.3938v1

Mathematics

Representation Theory

20pages

Scientific paper

In the previous paper "Symmetric Crystals and Affine Hecke Algebras of Type B", we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for $\gl_\infty$. In the first half of this paper (sections 2 and 3), we give a survey of the LLTA type theorem of the affine Hecke algebra of type $A$. In the latter half (sections 4, 5 and 6), we review the construction of the symmetric crystals and the LLTA type conjectures for the affine Hecke algebra of type $B$.

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