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Representation Theory of Finite Group Extensions: Clifford Theory, Mackey Obstruction, and the Orbit Method - Couverture souple
Synopsis
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 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.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
Tullio 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.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Representation Theory of Finite Group Extensions: Clifford Theory, Mackey Obstruction, and the Orbit Method (Springer Monographs in Mathematics)
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Representation Theory of Finite Group Extensions: Clifford Theory, Mackey Obstruction, and the Orbit Method (Springer Monographs in Mathematics)
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Representation Theory of Finite Group Extensions
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Springer International Publishing Nov 2023, 2023
ISBN 10 : 3031138759
ISBN 13 : 9783031138751
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 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. 356 pp. Englisch. N° de réf. du vendeur 9783031138751
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Representation Theory of Finite Group Extensions
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Springer International Publishing, 2023
ISBN 10 : 3031138759
ISBN 13 : 9783031138751
Neuf
Couverture souple
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The first monograph completely devoted to the representation theory of finite group extensionsIncludes new results on the projective representations of finite Abelian groups and their applicationsProvides a new, more operational and functio. N° de réf. du vendeur 1228908997
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Representation Theory of Finite Group Extensions | Clifford Theory, Mackey Obstruction, and the Orbit Method
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Taschenbuch. Etat : Neu. Representation Theory of Finite Group Extensions | Clifford Theory, Mackey Obstruction, and the Orbit Method | Tullio Ceccherini-Silberstein (u. a.) | Taschenbuch | xiii | Englisch | 2023 | Springer | EAN 9783031138751 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. N° de réf. du vendeur 128028921
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Representation Theory of Finite Group Extensions: Clifford Theory, Mackey Obstruction, and the Orbit Method (Springer Monographs in Mathematics)
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Representation Theory of Finite Group Extensions
ISBN 10 : 3031138759
ISBN 13 : 9783031138751
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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 356 pp. Englisch. N° de réf. du vendeur 9783031138751
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Representation Theory of Finite Group Extensions : Clifford Theory, Mackey Obstruction, and the Orbit Method
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Springer International Publishing, 2023
ISBN 10 : 3031138759
ISBN 13 : 9783031138751
Neuf
Taschenbuch
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 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. N° de réf. du vendeur 9783031138751
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Representation Theory of Finite Group Extensions: Clifford Theory, Mackey Obstruction, and the Orbit Method (Springer Monographs in Mathematics)
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Representation Theory of Finite Group Extensions: Clifford Theory, Mackey Obstruction, and the Orbit Method (Springer Monographs in Mathematics)
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