Realizations of the Irreducible Components of the Quasi-Regular Representation of Groups Transitive on Spheres. Invariant Subspaces

2009 ◽  
pp. 85-134
Author(s):  
Valery V. Volchkov ◽  
Vitaly V. Volchkov
Keyword(s):  
Regular Representation ◽  
Invariant Subspaces ◽  
Irreducible Components

scholarly journals GAUSSIAN FLUCTUATIONS OF REPRESENTATIONS OF WREATH PRODUCTS

2006 ◽  
Vol 09 (04) ◽  
pp. 529-546
Author(s):  
PIOTR ŚNIADY
Keyword(s):  
Finite Group ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Regular Representation ◽  
Wreath Products ◽  
Young Diagrams ◽  
Reducible Representation ◽  
Irreducible Components ◽  
Left Regular Representation ◽  
Left Regular

We study the asymptotics of the reducible representations of the wreath products G≀Sq = Gq ⋊ Sq for large q, where G is a fixed finite group and Sq is the symmetric group in q elements; in particular for G = ℤ/2ℤ we recover the hyperoctahedral groups. We decompose such a reducible representation of G≀Sq as a sum of irreducible components (or, equivalently, as a collection of tuples of Young diagrams) and we ask what is the character of a randomly chosen component (or, what are the shapes of Young diagrams in a randomly chosen tuple). Our main result is that for a large class of representations, the fluctuations of characters (and fluctuations of the shape of the Young diagrams) are asymptotically Gaussian. The considered class consists of the representations for which the characters asymptotically almost factorize and it includes, among others, the left regular representation therefore we prove the analogue of Kerov's central limit theorem for wreath products.

scholarly journals Discrete series of fusion algebras

2002 ◽  
Vol 72 (3) ◽  
pp. 419-426
Author(s):  
R. Srinivasan ◽  
V. S. Sunder ◽  
N. J. Wildberger
Keyword(s):  
Regular Representation ◽  
Discrete Series ◽  
Invariant Subspaces ◽  
Discrete Groups ◽  
Compact Lie Group ◽  
Finite Dimensional ◽  
Fusion Algebra ◽  
Left Regular Representation ◽  
Left Regular ◽  
Countably Infinite

AbstractWe show that the left regular representation of a countably infinite (discrete) group admits no finite-dimensional invariant subspaces. We also discuss a consequence of this fact, and the reason for our interest in this statement.We then formally state, as a ‘conjecture’, a possible generalisation of the above statement to the context of fusion algebras. We prove the validity of this conjecture in the case of the fusion algebra arising from the dual of a compact Lie group.We finally show, by example, that our conjecture is false as stated, and raise the question of whether there is a ‘good’ class of fusion algebras, which contains (a) the two ‘good classes’ discussed above, namely, discrete groups and compact group duals, and (b) only contains fusion algebras for which the conjecture is valid.

Invariant Subspaces on KPC-Hypergroups

2019 ◽  
Vol 15 (1) ◽  
pp. 122-130
Author(s):  
Laszlo Szekelyhidi ◽  
◽  
Seyyed Mohammad Tabatabaie ◽  
Keyword(s):  
Invariant Subspaces

Invariant Subspaces

1973 ◽  
Author(s):  
Heydar Radjavi ◽  
Peter Rosenthal
Keyword(s):  
Invariant Subspaces

scholarly journals Local rigidity for actions of Kazhdan groups on noncommutative Lp-spaces

2015 ◽  
Vol 26 (08) ◽  
pp. 1550064
Author(s):  
Bachir Bekka
Keyword(s):  
Von Neumann Algebra ◽  
Regular Representation ◽  
Von Neumann ◽  
Lp Spaces ◽  
Local Rigidity ◽  
Left Regular Representation ◽  
Left Regular ◽  
Property T ◽  
Finite Factor ◽  
Finite Index Subgroup

Let Γ be a discrete group and 𝒩 a finite factor, and assume that both have Kazhdan's Property (T). For p ∈ [1, +∞), p ≠ 2, let π : Γ →O(Lp(𝒩)) be a homomorphism to the group O(Lp(𝒩)) of linear bijective isometries of the Lp-space of 𝒩. There are two actions πl and πr of a finite index subgroup Γ+ of Γ by automorphisms of 𝒩 associated to π and given by πl(g)x = (π(g) 1)*π(g)(x) and πr(g)x = π(g)(x)(π(g) 1)* for g ∈ Γ+ and x ∈ 𝒩. Assume that πl and πr are ergodic. We prove that π is locally rigid, that is, the orbit of π under O(Lp(𝒩)) is open in Hom (Γ, O(Lp(𝒩))). As a corollary, we obtain that, if moreover Γ is an ICC group, then the embedding g ↦ Ad (λ(g)) is locally rigid in O(Lp(𝒩(Γ))), where 𝒩(Γ) is the von Neumann algebra generated by the left regular representation λ of Γ.

scholarly journals Shift-type invariant subspaces of contractions

2007 ◽  
Vol 246 (2) ◽  
pp. 281-301 ◽  
Author(s):  
László Kérchy
Keyword(s):  
Invariant Subspaces ◽  
Shift Type ◽  
Type Invariant
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