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SIGMA 10 (2014), 040, 11 pages arXiv:1312.6930
https://doi.org/10.3842/SIGMA.2014.040
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa
Mystic Reflection Groups
Yuri Bazlov a and Arkady Berenstein b
a) School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
b) Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
Received December 25, 2013, in final form March 24, 2014; Published online April 04, 2014
Abstract
This paper aims to systematically study mystic reflection groups that emerged independently in the
paper [Selecta Math. (N.S.) 14 (2009),
325-372] by the authors and in the paper [Algebr. Represent. Theory 13
(2010), 127-158] by Kirkman, Kuzmanovich and Zhang.
A detailed analysis of this class of groups reveals that they are in a nontrivial correspondence with the complex
reflection groups G(m,p,n).
We also prove that the group algebras of corresponding groups are isomorphic and classify all such groups up to
isomorphism.
Key words:
complex reflection; mystic reflection group; thick subgroups.
pdf (339 kb)
tex (16 kb)
References
- Bazlov Y., Berenstein A., Noncommutative Dunkl operators and braided
Cherednik algebras, Selecta Math. (N.S.) 14 (2009),
325-372, arXiv:0806.0867.
- Kirkman E., Kuzmanovich J., Zhang J.J., Shephard-Todd-Chevalley theorem
for skew polynomial rings, Algebr. Represent. Theory 13
(2010), 127-158, arXiv:0806.3210.
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