Leading coefficients of Kazhdan–Lusztig polynomials and fully commutative elements
نویسنده
چکیده
Let W be a Coxeter group of type ̃ An−1. We show that the leading coefficient, μ(x,w), of the Kazhdan–Lusztig polynomial Px,w is always equal to 0 or 1 if x is fully commutative (and w is arbitrary).
منابع مشابه
M ay 2 00 8 Leading coefficients of the Kazhdan - Lusztig polynomials for an Affine Weyl group of type
In this paper we compute the leading coefficients μ(y,w) of the Kazhdan-Lusztig polynomials Py,w for an affineWeyl group of type B̃2. When a(y) ≤ a(w) or a(y) = 2 and a(w) = 1, we compute all μ(y,w) clearly, where a(y) is the a-function of a Coxeter group defined by Lusztig (see [L1]). With these values μ(y,w), we are able to show that a conjecture of Lusztig on distinguished involutions is true...
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