Some power series involving involutions in Coxeter groups
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- by G. Lusztig
- Represent. Theory 19 (2015), 281-289
- DOI: https://doi.org/10.1090/ert/472
- Published electronically: November 4, 2015
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Abstract:
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.)References
- 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.
Bibliographic Information
- G. Lusztig
- Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Email: gyuri@math.mit.edu
- 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: https://doi.org/10.1090/ert/472
- MathSciNet review: 3418645