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- W4297730079 abstract "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 correspondence between the symmetric group and pairs of standard Young tableaux gives rise to a way to compute cells of Coxeter groups of type $A$. A lesser known correspondence exists for signed permutations and pairs of so-called domino tableaux, which allows us to compute cells in Coxeter groups of types $B$ and $D$. I will use this correspondence in type $D$ to compute $mu$-values involving bad elements. I will conclude by showing that $mu(x,w)$ is 0 or 1 when $x$ is fully commutative in type $D$." @default.
- W4297730079 created "2022-09-30" @default.
- W4297730079 creator A5078610602 @default.
- W4297730079 date "2013-04-22" @default.
- W4297730079 modified "2023-09-25" @default.
- W4297730079 title "Leading Coefficients of Kazhdan--Lusztig Polynomials in Type $D$" @default.
- W4297730079 doi "https://doi.org/10.48550/arxiv.1304.6074" @default.
- W4297730079 hasPublicationYear "2013" @default.
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