Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras
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- by Arkady Berenstein and Yurii Burman PDF
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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.References
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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
- 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 - © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2550150