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Noncommutative Dunkl operators and braided Cherednik algebras.
- Source :
-
Selecta Mathematica, New Series . May2009, Vol. 14 Issue 3/4, p325-372. 48p. - Publication Year :
- 2009
-
Abstract
- Abstract.  We introduce braided Dunkl operators $$\underline{\nabla}_1,\ldots,\underline{\nabla}_n$$ that act on a q-symmetric algebra $$S_{\bf q}({\mathbb{C}}^n)$$ and q-commute. Generalising the approach of Etingof and Ginzburg, we explain the q-commutation phenomenon by constructing braided Cherednik algebras $$\underline{{\mathcal{H}}}$$ for which the above operators form a representation. We classify all braided Cherednik algebras using the theory of braided doubles developed in our previous paper. Besides ordinary rational Cherednik algebras, our classification gives new algebras $$\underline{{\mathcal{H}}}(W_+)$$ attached to an infinite family of subgroups of even elements in complex reflection groups, so that the corresponding braided Dunkl operators $$\underline{\nabla}_i$$ pairwise anticommute. We explicitly compute these new operators in terms of braided partial derivatives and W+-divided differences. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10221824
- Volume :
- 14
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Selecta Mathematica, New Series
- Publication Type :
- Academic Journal
- Accession number :
- 39989290
- Full Text :
- https://doi.org/10.1007/s00029-009-0525-x