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Mystic Reflection Groups
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Mystic Reflection Groups
Інший ID:
2010 Mathematics Subject Classification: 16G99; 20F55; 16S80
DOI:10.3842/SIGMA.2014.040
DOI:10.3842/SIGMA.2014.040
Посилання:
Mystic Reflection Groups / Y. Bazlov, A. Berenstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 2 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full
collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html.
We thank Ken Brown for bringing the paper [2] to our attention, and Alexander Premet for
stimulating discussions. The present paper was started when both authors were research members
of the Mathematical Sciences Research Institute. We thank the Institute and the organizers
of the Noncommutative Algebraic Geometry and Representation Theory program for creating
an atmosphere conducive for research. We acknowledge partial support of the LMS Research
in Pairs grant ref. 41224. The second named author was partially supported by the NSF grant
DMS-1101507.
Дата:
2014
Переглядів:
523
Завантажень:
270
Анотація:
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.
