Corpus ID: 117772614

# Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D

@article{Gern2013LeadingCO,
title={Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D},
author={Tyson C. Gern},
journal={arXiv: Combinatorics},
year={2013}
}
Kazhdan--Lusztig polynomials arise in the context of Hecke algebras associated to Coxeter groups. The computation of these polynomials is very difficult for examples of even moderate rank. In type $A$ it is known that the leading coefficient, $\mu(x,w)$ of a Kazhdan--Lusztig polynomial $P_{x,w}$ is either 0 or 1 when $x$ is fully commutative and $w$ is arbitrary. In type $D$ Coxeter groups there are certain "bad" elements that make $\mu$-value computation difficult. The Robinson--Schensted… Expand
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