Representations of the alternating group which are irreducible over subgroups, II

Representations of the Alternating Group Which Are Irreducible over Subgroups

Representations of the General Linear Groups Which Are Irreducible over Subgroups

1.1. Aschbacher-Scott Program. Primitive permutation groups have been studied since Galois and Jordan and have applications in many different areas. If Γ is a transitive permutation group with a point stabilizer M then Γ is primitive if and only if M < Γ is a maximal subgroup. So studying primitive permutation groups is equivalent to studying maximal subgroups. In most problems involving a fini...

ON THE IRREDUCIBLE REPRESENTATIONS OF THE ALTERNATING GROUP WHICH REMAIN IRREDUCIBLE IN CHARACTERISTIC p

We consider the problem of which ordinary irreducible representations of the alternating group An remain irreducible modulo a prime p. We solve this problem for p = 2, and present a conjecture for odd p, which we prove in one direction.

Irreducible representations of crossed products of the Cuntz algebras and isotropy subgroups of the unitary group

For an element x of the Cuntz algebra ON , define the isotropy subgroup Gx ≡ {g ∈ U(N) : αg(x) = x} of the unitary group U(N) with respect to the canonical action α of U(N) on ON . We have irreducible representations of the crossed product ONoGx by extending irreducible generalized permutative representations of ON and irreducible representation of Gx. ¿From this, the Peter-Weyl theorem for Gx ...

Representations of the Symmetric Group Are Reducible over Singly Transitive Subgroups