
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),
325372] by the authors and in the paper [Algebr. Represent. Theory 13
(2010), 127158] 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),
325372, arXiv:0806.0867.
 Kirkman E., Kuzmanovich J., Zhang J.J., ShephardToddChevalley theorem
for skew polynomial rings, Algebr. Represent. Theory 13
(2010), 127158, arXiv:0806.3210.

