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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Poincaré series of subsets of affine Weyl groups


Author: Sankaran Viswanath
Journal: Proc. Amer. Math. Soc. 136 (2008), 3735-3740
MSC (2000): Primary 05E15
Published electronically: June 17, 2008
MathSciNet review: 2425710
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Abstract: In this note, we identify a natural class of subsets of affine Weyl groups whose Poincaré series are rational functions. This class includes the sets of minimal coset representatives of reflection subgroups. As an application, we construct a generalization of the classical length-descent generating function and prove its rationality.


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Additional Information

Sankaran Viswanath
Affiliation: Department of Mathematics, University of California, Davis, California 95616
Address at time of publication: Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Email: svis@math.iisc.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09382-9
PII: S 0002-9939(08)09382-9
Keywords: Rational function, descent, reflection subgroup
Received by editor(s): August 1, 2006
Published electronically: June 17, 2008
Communicated by: Jim Haglund
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.