Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 10 (2014), 040, 11 pages      arXiv:1312.6930      http://dx.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.

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References

  1. Bazlov Y., Berenstein A., Noncommutative Dunkl operators and braided Cherednik algebras, Selecta Math. (N.S.) 14 (2009), 325-372, arXiv:0806.0867.
  2. 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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