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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2014 Volume 10, 040, 11 pp. (Mi sigma905)

This article is cited in 5 papers

Mystic Reflection Groups

Yuri Bazlova, Arkady Berenshteinb

a School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
b Department of Mathematics, University of Oregon, Eugene, OR 97403, USA

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.

Keywords: complex reflection; mystic reflection group; thick subgroups.

MSC: 16G99; 20F55; 16S80

Received: December 25, 2013; in final form March 24, 2014; Published online April 4, 2014

Language: English

DOI: 10.3842/SIGMA.2014.040



Bibliographic databases:
ArXiv: 1312.6930


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