Irreducibility of certain unitary representations

Irreducibility of certain pseudovarieties 1

We prove that the pseudovarieties of all finite semigroups, and of all aperiodic fin1 e sernigroups are irreducible for join, for semidirect product and for hlal 'ce~. product. In particular, these pseudovarieties do not admit maximal proper suhpseudovariet~es. More generally, analogous results are proved for the pseudovar~ety of all finite serrigroups all of whose subgroups are in a fixed pseu...

On the Existence and Irreducibility of Certain Series of Representations by Bertram Kostant

Permutation representations and rational irreducibility

The natural character π of a finite transitive permutation group G has the form 1G + θ where θ is a character which affords a rational representation of G. We call G a QI-group if this representation is irreducible over Q. Every 2-transitive group is a QI-group, but the latter class of groups is larger. It is shown that every QI-group is 3/2transitive and primitive, and that it is either almost...

Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$

‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$‎. ‎We then determine necessary and sufficient conditions that guarantee the irreducibility of th...

Transfer of Unitary Representations

Introduction. This paper has as its primary purpose a clear exposition of the idea in [21] which we describe as transfer between real forms of a semi-simple Lie group over C. The basic point is that there are representations of one real form that can be more easily understood in the context of another real from. An interesting example is a minimal representation (that is annihilated by the Jose...