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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups
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by Patrick Polo
Represent. Theory 3 (1999), 90-104
Published electronically: June 22, 1999


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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Bibliographic 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