| 书目名称 | Representation Theory of Finite Group Extensions | | 副标题 | Clifford Theory, Mac | | 编辑 | Tullio Ceccherini-Silberstein,Fabio Scarabotti,Fil | | 视频video | | | 概述 | The first monograph completely devoted to the representation theory of finite group extensions.Includes new results on the projective representations of finite Abelian groups and their applications.Pr | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | 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. ..TheLittle 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 correspond | | 出版日期 | Book 2022 | | 关键词 | Induced representation; Unitary Representation; Projective Representation; Orbit Method; Mackey Obstruct | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-13873-7 | | isbn_softcover | 978-3-031-13875-1 | | isbn_ebook | 978-3-031-13873-7Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 17:51:58
