Weak containment and induced representations of groups. II

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

Weak Containment and Rokhlin Entropy

We define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies. This leads to new upper bounds to Rokhlin entropy. We also use this notion to study how Pinsker algebras behave under direct products, and we study the Rokhlin entropy of restricted actions of finite-index subgroups.

Lecture 2: Representations of Symmetric Groups, Ii

Recall that last time we have introduced the set of weights Wt(n) ⊂ C and an equivalence relation ∼ on Wt(n). Our goal is to describe this set and this equivalence relation – the equivalence classes are in a natural bijection with Irr(Sn). The first step here is as follows. Pick a path P = V 1 → V 2 → . . . → V n in the branching graph and an integer k with 1 < k < n. We fix all vertices but V ...

Projective Representations of Reflection Groups Ii