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Noncommutative Dunkl operators and braided Cherednik algebras

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Bazlov, Yuri and Berenstein, Arkady (2009) Noncommutative Dunkl operators and braided Cherednik algebras. In: Conference on Cherednik Algebras Conference, Univ Edinburgh, Edinburgh, Scotland, JUN, 2007. Published in: Selecta Mathematica, New Series, Vol.14 (No.3-4). pp. 325-372. doi:10.1007/s00029-009-0525-x ISSN 1022-1824.

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Official URL: http://dx.doi.org/10.1007/s00029-009-0525-x

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Abstract

We introduce braided Dunkl operators (del) under bar (1), ... ,(del) under bar (n) that act on a q-symmetric algebra S-q (C-n) and q-commute. Generalising the approach of Etingof and Ginzburg, we explain the q-commutation phenomenon by constructing braided Cherednik algebras (H) under bar 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 (H) under bar (W+) attached to an in finite family of subgroups of even elements in complex reflection groups, so that the corresponding braided Dunkl operators (del) under bar (i) pairwise anticommute. We explicitly compute these new operators in terms of braided partial derivatives and W+-divided differences.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Selecta Mathematica, New Series
Publisher: Birkhauser Verlag AG
ISSN: 1022-1824
Official Date: May 2009
Dates:
DateEvent
May 2009Published
Volume: Vol.14
Number: No.3-4
Number of Pages: 48
Page Range: pp. 325-372
DOI: 10.1007/s00029-009-0525-x
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Conference Paper Type: Paper
Title of Event: Conference on Cherednik Algebras Conference
Type of Event: Conference
Location of Event: Univ Edinburgh, Edinburgh, Scotland
Date(s) of Event: JUN, 2007

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