of the American Mathematical Society

Thomas Braden

(University of Massachusetts, Amherst)

## Lower bounds for Kazhdan-Lusztig polynomials from patterns

Abstract[ps] [pdf]:If $x$ and $y$ are elements of a Weyl group $W$, and $W'$ is a subgroup of $W$ generated by reflections, we give lower bounds for $P_{x,w}(1)$ in terms of the cosets containing $x$ and $w$ and their positions within those cosets. If $W = S_n$ this relates to pattern avoidance -- e.g. we get $P_{1,w}(1) \ge P_{1,y}(1)$ where $y$ is any pattern contained in $w$.This is joint work with Sara Billey.

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last updated: August 21, 2001