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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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A simple combinatorial proof of a generalization of a result of Polo
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by Fabrizio Caselli PDF
Represent. Theory 8 (2004), 479-486 Request permission

Abstract:

We provide a simple combinatorial proof of, and generalize, a theorem of Polo which asserts that for any polynomial $P\in \mathbb N[q]$ such that $P(0)=1$ there exist two permutations $u$ and $v$ in a suitable symmetric group such that $P$ is equal to the Kazhdan-Lusztig polynomial $P^{v}_{u}$.
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Additional Information
  • Fabrizio Caselli
  • Affiliation: Università di Roma “La Sapienza”, Dipartimento di matematica “G. Castelnuovo”, P.le A. Moro 3, 00185, Roma, Italy
  • Email: caselli@mat.uniroma1.it and caselli@igd.univ-lyon1.fr
  • Received by editor(s): July 30, 2003
  • Received by editor(s) in revised form: March 19, 2004, and July 25, 2004
  • Published electronically: November 2, 2004
  • Additional Notes: The author was partially supported by EC grant HPRN-CT-2002-00272
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 8 (2004), 479-486
  • MSC (2000): Primary 05E15, 20C08
  • DOI: https://doi.org/10.1090/S1088-4165-04-00203-1
  • MathSciNet review: 2110357