# Category: Unitary representation theory

Representative function
No description available.
Gårding domain
In mathematics, a Gårding domain is a concept in the representation theory of topological groups. The concept is named after the mathematician Lars Gårding. Let G be a topological group and let U be a
Kazhdan's property (T)
In mathematics, a locally compact topological group G has property (T) if the trivial representation is an isolated point in its unitary dual equipped with the Fell topology. Informally, this means th
System of imprimitivity
The concept of system of imprimitivity is used in mathematics, particularly in algebra and analysis, both within the context of the theory of group representations. It was used by George Mackey as the
Peter–Weyl theorem
In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian. It was initially proved b
Tannaka–Krein duality
In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is a natural extension of Pontryagin duality, betwee
Isotypical representation
In group theory, an isotypical, primary or factor representation of a group G is a unitary representation such that any two subrepresentations have equivalent sub-subrepresentations. This is related t
Quasiregular representation
This article addresses the notion of quasiregularity in the context of representation theory and topological algebra. For other notions of quasiregularity in mathematics, see the disambiguation page q
Unitary representation
In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-de
Mautner's lemma
In mathematics, Mautner's lemma in representation theory states that if G is a topological group and π a unitary representation of G on a Hilbert space H, then for any x in G, which has conjugates yxy
Principal series representation
In mathematics, the principal series representations of certain kinds of topological group G occur in the case where G is not a compact group. There, by analogy with spectral theory, one expects that
Group algebra of a locally compact group
In functional analysis and related areas of mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra)