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Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras


Authors: Arkady Berenstein and Yurii Burman
Journal: Trans. Amer. Math. Soc. 362 (2010), 229-260
MSC (2000): Primary 20F55; Secondary 15A72
DOI: https://doi.org/10.1090/S0002-9947-09-04620-0
Published electronically: August 17, 2009
MathSciNet review: 2550150
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Abstract: We introduce and study deformations of finite-dimensional modules over rational Cherednik algebras. Our main tool is a generalization of usual harmonic polynomials for each Coxeter group -- the so-called quasiharmonic polynomials. A surprising application of this approach is the construction of canonical elementary symmetric polynomials and their deformations for all Coxeter groups.


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Additional Information

Arkady Berenstein
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: arkadiy@math.uoregon.edu

Yurii Burman
Affiliation: Department of Mathematics, Independent University of Moscow, 121002, 11, B.Vlassievsky per., Moscow, Russia
Address at time of publication: Higher School of Economics, 101000, 20, Myasnitskaya str., Moscow, Russia
Email: burman@mccme.ru

DOI: https://doi.org/10.1090/S0002-9947-09-04620-0
Received by editor(s): January 29, 2007
Received by editor(s) in revised form: August 24, 2007
Published electronically: August 17, 2009
Additional Notes: The first author’s research was supported in part by the NSF (DMS) grants #0102382 and #0501103
The second author’s research was supported by RFBR grants #N.Sh.4719.2006.1 and #05-01-01012a
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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