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Representation theory of finite grou...

Ceccherini-Silberstein, Tullio.

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Representation theory of finite group extensions = Cclifford theory, Mackey obstruction, and the orbit method /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Representation theory of finite group extensions/ by Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli.
其他題名:	Cclifford theory, Mackey obstruction, and the orbit method /
作者:	Ceccherini-Silberstein, Tullio.
其他作者:	Scarabotti, Fabio.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xiii, 340 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Representations of groups. -
電子資源:	https://doi.org/10.1007/978-3-031-13873-7
ISBN:	9783031138737

Representation theory of finite group extensions = Cclifford theory, Mackey obstruction, and the orbit method /
Ceccherini-Silberstein, Tullio.

Representation theory of finite group extensionsCclifford theory, Mackey obstruction, and the orbit method /[electronic resource] :by Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli. - Cham :Springer International Publishing :2022. - xiii, 340 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

This monograph adopts an operational and functional analytic approach to the following problem: given a short exact sequence (group extension) 1 → N → G → H → 1 of finite groups, describe the irreducible representations of G by means of the structure of the group extension. This problem has attracted many mathematicians, including I. Schur, A.H. Clifford, and G. Mackey and, more recently, M. Isaacs, B. Huppert, Y.G. Berkovich & E.M. Zhmud, and J.M.G. Fell & R.S. Doran. The main topics are, on the one hand, Clifford Theory and the Little Group Method (of Mackey and Wigner) for induced representations, and, on the other hand, Kirillov's Orbit Method (for step-2 nilpotent groups of odd order) which establishes a natural and powerful correspondence between Lie rings and nilpotent groups. As an application, a detailed description is given of the representation theory of the alternating groups, of metacyclic, quaternionic, dihedral groups, and of the (finite) Heisenberg group. The Little Group Method may be applied if and only if a suitable unitary 2-cocycle (the Mackey obstruction) is trivial. To overcome this obstacle, (unitary) projective representations are introduced and corresponding Mackey and Clifford theories are developed. The commutant of an induced representation and the relative Hecke algebra is also examined. Finally, there is a comprehensive exposition of the theory of projective representations for finite Abelian groups which is applied to obtain a complete description of the irreducible representations of finite metabelian groups of odd order.

ISBN: 9783031138737

Standard No.: 10.1007/978-3-031-13873-7doiSubjects--Topical Terms:

519598
Representations of groups.

LC Class. No.: QA176

Dewey Class. No.: 512.22

Representation theory of finite group extensions = Cclifford theory, Mackey obstruction, and the orbit method /
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