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Representation Theory

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Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups

Author: Patrick Polo
Journal: Represent. Theory 3 (1999), 90-104
MSC (1991): Primary 14M15; Secondary 20F55, 20G15
Published electronically: June 22, 1999
MathSciNet review: 1698201
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Abstract: To each polynomial $P$ with integral nonnegative coefficients and constant term equal to $1$, of degree $d$, we associate a certain pair of elements $(y,w)$ in the symmetric group $S_n$, where $n = 1 + d + P(1)$, such that the Kazhdan-Lusztig polynomial $P_{y,w}$ equals $P$. This pair satisfies $\ell (w) - \ell (y) = 2d + P(1) - 1$, where $\ell (w)$ denotes the number of inversions of $w$.

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Patrick Polo
Affiliation: CNRS, UMR 7539, Institut Galilée, Département de mathématiques, Université Paris-Nord, 93430 Villetaneuse, France

Received by editor(s): December 11, 1998
Received by editor(s) in revised form: April 30, 1999
Published electronically: June 22, 1999
Article copyright: © Copyright 1999 American Mathematical Society