Geodesic
Mystic Reflection Groups
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2014_10_a39,
     author = {Yuri Bazlov and Arkady Berenshtein},
     title = {Mystic {Reflection} {Groups}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
     volume = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a39/}
}
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Yuri Bazlov; Arkady Berenshtein. Mystic Reflection Groups. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a39/

[1] Bazlov Y., Berenstein A., “Noncommutative {D}unkl operators and braided {C}herednik algebras”, Selecta Math. (N.S.), 14 (2009), 325–372, arXiv: 0806.0867 | DOI | MR | Zbl

[2] Kirkman E., Kuzmanovich J., Zhang J. J., “Shephard–{T}odd–{C}hevalley theorem for skew polynomial rings”, Algebr. Represent. Theory, 13 (2010), 127–158, arXiv: 0806.3210 | DOI | MR | Zbl