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OverviewThis 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 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. Full Product DetailsAuthor: Tullio Ceccherini-Silberstein , Fabio Scarabotti , Filippo TolliPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2022 Weight: 0.699kg ISBN: 9783031138720ISBN 10: 3031138724 Pages: 340 Publication Date: 30 November 2022 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents- 1. Preliminaries. - 2. Clifford Theory. - 3. Abelian Extensions. - 4. The Little Group Method for Abelian Extensions. - 5. Examples and Applications. - 6. Central Extensions and the Orbit Method. - 7. Representations of Finite Group Extensions via Projective Representations. - 8. Induced Projective Representations. - 9. Clifford Theory for Projective Representations. - 10 Projective Representations of Finite Abelian Groups with Applications.ReviewsAuthor InformationTullio Ceccherini-Silberstein obtained his BS in Mathematics (1990) from the University of Rome “La Sapienza” and his PhD in Mathematics (1994) from UCLA. Currently, he is professor of Mathematical Analysis at the University of Sannio (Benevento). He is an Editor of the EMS journal “Groups, Geometry, and Dynamics” and of the Bulletin of the Iranian Mathematical Society. He has authored more than 90 research articles in Functional and Harmonic Analysis, Group Theory, Ergodic Theory and Dynamical Systems, and Theoretical Computer Science and has co-authored 9 monographs on Harmonic Analysis and Representation Theory and on Group Theory and Dynamical Systems. Fabio Scarabotti obtained his BS in Mathematics (1989) and his PhD in Mathematics (1994) from the University of Rome “La Sapienza”. Currently, he is professor of Mathematical Analysis at the University of Rome “La Sapienza”. He has authored more than 40 research articles in Harmonic Analysis, Group Theory, Combinatorics, Ergodic Theory and Dynamical Systems, and Theoretical Computer Science and has co-authored 6 monographs on Harmonic Analysis and Representation Theory. Filippo Tolli obtained his BS in Mathematics (1991) from the University of Rome “La Sapienza” and his PhD in Mathematics (1996) from UCLA. Currently, he is professor of Mathematical Analysis at the University of Roma Tre. He has authored more than 30 research articles in Harmonic Analysis, Group Theory, Combinatorics, Lie Groups and Partial Differential Equations and has co-authored 6 monographs on Harmonic Analysis and Representation Theory. Tab Content 6Author Website:Countries AvailableAll regions |
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