Some multiplication formulas in an affine Hecke algebra

2010/03/25 by Wang, Liping
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1003.4817

Abstract

In this paper we consider the Hecke algebra \mathcal H associated to an extended affine Weyl group of type \widetildeB₂. We give some interesting formulas on C_rtS_λ, which imply some relations between the Kazhdan-Lusztig coefficients μ(y,w) and representations of some algebraic groups. Here C_rt is one element in the Kazhdan-Lusztig basis of \mathcal H and S_λ is an element in the center of \mathcal H.

Related

• The based ring of the lowest two-sided cell of an affine Weyl group, III
• Multiplicity matrices for the affine graded Hecke algebra
• Kazhdan-Lusztig coefficients for an Affine Weyl group of type \widetildeA₂
• Non-trivial Kazhdan-Lusztig coefficients of affine Weyl groups
• Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type \widetildeB₂