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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups
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by Patrick Polo PDF
Represent. Theory 3 (1999), 90-104 Request permission


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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Additional Information
  • Patrick Polo
  • Affiliation: CNRS, UMR 7539, Institut Galilée, Département de mathématiques, Université Paris-Nord, 93430 Villetaneuse, France
  • Email:
  • Received by editor(s): December 11, 1998
  • Received by editor(s) in revised form: April 30, 1999
  • Published electronically: June 22, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 90-104
  • MSC (1991): Primary 14M15; Secondary 20F55, 20G15
  • DOI:
  • MathSciNet review: 1698201