1,720,976 research outputs found
Radon transforms and lamplighter random walks.
Get PDFWe use a Radon transform approach to compute the spectrum of the lamplighter random walk on the pat
A note on the Kaloujnine-Krasner theorem
No full textThe celebrated Kaloujnine-Krasner theorem associates, with a short exact sequence 1 -> N -> (iota) G -> (pi) H -> 1 of groups and a section s:H -> G, an embedding Phi : G -> N(sic)H of G into the (unrestricted) wreath product of N and H. Given two groups H and N, a short exact sequence as above is called an extension of H by N, denoted by (G;iota,pi). Moreover, one says that two extensions (G(1);iota(1),pi(1)) and (G(2);iota(2),pi(2)) of H by N are equivalent if there exists a group isomorphism eta : G(1) -> G(2) such that iota(2)=eta circle iota(1) and pi(1)=pi(2)circle eta. We say that two embeddings Phi(1):G(1) -> N(sic)H and Phi(2):G(2)-> N(sic)H are equivalent if there exists a group isomorphism eta : G(1) -> G(2) such that Phi(1)=Phi(2) circle eta. We show that two extensions (G(1);iota(1),pi(1)) and (G(2);iota(2),pi(2)) are equivalent if and only if the embeddings Phi(1) and Phi(2), associated with any two sections s(1 ): H -> G(1) and s(2 ): H -> G(2) via the Kaloujnine-Krasner theorem, are equivalent
Abelian extensions
No full textThis chapter is based on (Canad J Math 23:857–865, 1971; Canad J Math 25:1113–1119, 1973) by R. L. Roth. Previous papers with some results on this subject include (J. Fac. Sci. Univ. Tokyo Sec. I 10:129–146, 1964) (Pacific J Math 32:119–129, 1970) by N. Iwahori – H. Matsumoto and G. J. Janusz, respectively. See also Sect. 2.4, where the more general case when G∕IG(σ) is Abelian was studied
Gelfand triples and their hecke algebras: harmonic analysis for multiplicity-free induced representations of finite groups
No full textTriple di Gelfand e loro algebre di HeckeGelfand triple and their Hecke algebra
Representation theory of finite group extensions Clifford theory, Mackey obstruction, and the orbit method
No full textRepresentation Theory of Finite Group Extensions, Clifford Theory, Mackey Obstruction and Orbit Metho
Projective representations of finite abelian groups with applications
No full textIn this chapter, we describe the irreducible projective representations of a finite Abelian group: we shall use the Clifford theory from the previous chapter. Then, by means of the machinery developed in Sect. 7.3, we describe the ordinary, irreducible representations of finite metabelian groups. As a particular case, we obtain an alternative description of the irreducible representations of finite 2-step nilpotent groups (cf. Sect. 6.6 )
Hecke algebras
Get PDFSia G un gruppo finito e K un sottogruppo. Dalla similarità tra rappresentazioni indotte e rappresentazioni permutazionali abbiamo un isomorfismo tra l'algebra delle funzioni bi-K-invarianti su G e il commutante della rappresentazione ottenuta inducendo la banale da K a G.Let G be a finite group and K ≤ G a subgroup. Recalling the equality between the induced representation (IndKGιK,IndKGC) and the permutation representation (λ, L(G)K), (1.11) yields a ∗-algebra isomorphism between the algebra of bi-K-invariant functions on G and the commutant of the representation obtained by inducing to G the trivial representation of K
Induced representations and Mackey theory
Get PDFThis is an exposition on Mackey theory for induced representations of finite group
Central Extensions and the Orbit Method
No full textIn this chapter we treat central extensions of groups, a particular case of the construction in Sect. 1.5, and we give a complete cohomological characterization of these. Following Mihailovs (The orbit method for finite groups of nilpotency class two of odd order. Preprint: arXiv.org: math.RT/0001092) and Kokhas (J Math Sci (NY) 131(2):5508–5555, 2004) with a 2-step nilpotent group with 2-divisible center we associate a 2-step nilpotent Lie ring. This is a key construction for the definition and application of the orbit method
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