particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself...

p-groups Regular prime, a prime number p > 2 that does not divide the class number of the p-th cyclotomic field The regular representation of a group...

L_{s}} is a unitary representation of G . {\displaystyle G.} It is called left-regular representation. The right-regular representation is defined similarly...

image of T, which is the subgroup K. T is sometimes called the regular representation of G. An alternative setting uses the language of group actions...

are not tempered and do not appear in the decomposition of the regular representation into irreducible representations. They are rather mysterious: they...

is a closed subgroup. In line with the concepts of regular representation and induced representation, G acts on functions on G/H. If however Haar measures...

induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of H...

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...

matrix to any element of the field K {\displaystyle K} is called the regular representation. The square matrix A {\displaystyle A} represents the effect of...

In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or...

intuitive way to understand this version is that the support of the regular representation is the whole space of irreducible representations. In discrete group...

case every irreducible representation is a direct summand of the regular representation, hence is projective. Modular representation theory was developed...

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of...

series representation is an irreducible unitary representation of a locally compact topological group G that is a subrepresentation of the left regular representation...

A regular expression (shortened as regex or regexp), sometimes referred to as rational expression, is a sequence of characters that specifies a match...

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra...

X as a left regular representation: ( g ⋅ f ) ( x ) = f ( g − 1 x ) {\displaystyle (g\cdot f)(x)=f(g^{-1}x)} . This is a representation of G on the coordinate...

R and R[G] modules, it is the regular representation of the group. Written as a representation, it is the representation g ↦ ρg with the action given by...

generalizing the significant facts about the decomposition of the regular representation of any finite group, as discovered by Ferdinand Georg Frobenius...

M. If M is a left ideal of A then the left regular representation Φ on M now descends to a representation Φ' on the quotient vector space A/M. If [b]...

I\}),} the left regular representation of the Lorentz group, and L 2 ( G / K ) , {\displaystyle L^{2}(G/K),} the regular representation on 3-dimensional...

specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation of a group...

the (n − 1)-dimensional representation is reducible – the permutation representation coincides with the regular representation, and thus breaks up into...

permutation group acting on itself by translation, one obtains the regular representation. Given a group G {\displaystyle G} and a finite set X {\displaystyle...

structure. The Cayley–Dickson construction is closely related to the regular representation of C , {\displaystyle \mathbb {C} ,} thought of as an R {\displaystyle...

In mathematics, a tempered representation of a linear semisimple Lie group is a representation that has a basis whose matrix coefficients lie in the Lp...

group. There, by analogy with spectral theory, one expects that the regular representation of G will decompose according to some kind of continuous spectrum...

representation of G. As an abstract group, G is known as the cyclic group C4, and this permutation representation of it is its regular representation...

generalized to quasi-Frobenius rings, those Noetherian rings whose right regular representation is injective. In recent times, interest has been renewed in Frobenius...

forms. Harish-Chandra used Eisenstein integrals to decompose the regular representation of a semisimple Lie group into representations induced from parabolic...