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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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Some power series involving involutions in Coxeter groups
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by G. Lusztig PDF
Represent. Theory 19 (2015), 281-289 Request permission


Let $W$ be a Coxeter group. We show that a certain power series involving a sum over all involutions in $W$ can be expressed in terms of the Poincaré series of $W$. (The case where $W$ is finite has been known earlier.)
  • G. Lusztig, A bar operator for involutions in a Coxeter group, Bull. Inst. Math. Acad. Sin. (N.S.) 7 (2012), no. 3, 355–404. MR 3051318
  • G. Lusztig, Hecke algebras with unequal parameters, CRM Monograph Series, vol. 18, American Mathematical Society, Providence, RI, 2003. MR 1974442, DOI 10.1090/crmm/018
  • George Lusztig and David A. Vogan Jr., Hecke algebras and involutions in Weyl groups, Bull. Inst. Math. Acad. Sin. (N.S.) 7 (2012), no. 3, 323–354. MR 3051317
  • E. Marberg and G. White, Variations of the Poincaré series for the affine Weyl groups and $q$-analogues of Chebyshev polynomials, arxiv:1410.2772.
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • Received by editor(s): June 15, 2015
  • Received by editor(s) in revised form: October 17, 2015
  • Published electronically: November 4, 2015
  • Additional Notes: Supported in part by National Science Foundation grant DMS-1303060 and by a Simons Fellowship.
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 281-289
  • MSC (2010): Primary 20G99
  • DOI:
  • MathSciNet review: 3418645