Extending irreducible representations of normal subgroups

Representations of the Alternating Group Which Are Irreducible over Subgroups

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 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...

Classifying fuzzy normal subgroups of finite groups

In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

Understanding Irreducible Representations

This paper acts as an introduction to representation theory. In addition to defining representations of Lie algebras and of finite groups, this paper will go through two standard examples, the Lie algebra sl2C and the finite group Sn, to illustrate techniques for their construction and use. In addition, those examples will develop some important theory behind representations of Lie algebras and...