Abstract
This study focusses on the leading coefficients μ u , w of the Kazhdan–Lusztig polynomials P u , w for the lowest cell c 0 of an affine Weyl group of type G 2 ˜ and gives an estimation μ u , w ≤ 3 for u , w ∈ c 0 .
Highlights
Introduction e Hecke algebraH of the Coxeter group W over Z[q(1/2), q− (1/2)] is a free A-module and has a basis Tww∈W
Its multiplication is defined by the relations (Ts − q)(Ts + 1) 0 if s ∈ S and TwTu Twu if l(wu) l(w) + l(u). e combination Cw q− (l(w)/2)u≤wPu,wTu, w ∈ W be its Kazhdan–Lusztig basis, where Pu,w ∈ Z[q](u ≤ w) are the Kazhdan–Lusztig polynomials. e degree of Pu,w is less than or equal to (1/2)(l(w) − l(u) − 1) if u < w and Pw,w 1. e subalgebra H of H generated by all Ts(s ∈ S) is the Hecke algebra of the Coxeter system (W, S)
We describe our algorithm in order to compute Kazhdan–Lusztig polynomials for the affine Weyl group and some special multiplications of Kazhdan–Lusztig basis
Summary
Introduction e Hecke algebraH of the Coxeter group W over Z[q(1/2), q− (1/2)] is a free A-module and has a basis Tww∈W. We describe our algorithm in order to compute Kazhdan–Lusztig polynomials for the affine Weyl group and some special multiplications of Kazhdan–Lusztig basis.
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