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.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
