Leading coefficients of Kazhdan--Lusztig polynomials and fully commutative elements

Details Leading coefficients of Kazhdan--Lusztig polynomials and fully commutative elements Leading coefficients of Kazhdan--Lusztig polynomials and fully commutative elements

2008-01-10

arxiv.org/abs/0801.1650v1

Mathematics

Quantum Algebra

Approximately 10 pages, AMSTeX

Scientific paper

Let $W$ be a Coxeter group of type $\widetilde{A}_{n-1}$. We show that the
leading coefficient, $\mu(x, w)$, of the Kazhdan--Lusztig polynomial $P_{x, w}$
is always equal to 0 or 1 if $x$ is fully commutative (and $w$ is arbitrary).

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