Process of extending a representation of a subgroup to the parent group
In group theory, the 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, the induced representation is, in a sense, the "most general" representation of G that extends the given one. Since it is often easier to find representations of the smaller group H than of G, the operation of forming induced representations is an important tool to construct new representations.
Induced representations were initially defined by Frobenius, for linear representations of finite groups. The idea is by no means limited to the case of finite groups, but the theory in that case is particularly well-behaved.
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inducedrepresentation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of...
(ks).} The inducedrepresentation is then again a unitary representation. Since G {\displaystyle G} is compact, the inducedrepresentation can be decomposed...
the character of the induced representation V of G. The basic result on induced characters is Brauer's theorem on induced characters. It states that every...
induction Backward induction in game theory and economics Inducedrepresentation, in representation theory Mathematical induction, a method of proof Strong...
Zeeman effect. The inducedrepresentation is a related operation that forms a representation of the whole group from a representation of a subgroup. The...
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...
module theory, the induced module K [ G ] ⊗ K [ H ] M {\displaystyle K[G]\otimes _{K[H]}M} corresponds to the inducedrepresentation Ind H G {\displaystyle...
that inducedrepresentation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of...
with induced representations is that the permutation representation on cosets is the special case of inducedrepresentation, in which a representation is...
the representation breaks up into discrete summands. Here the trace formula is an extension of the Frobenius formula for the character of an induced representation...
theorem Representation of a Lie group Unitary representation Irreducible representation Harish-Chandra character Restricted representationInduced representation...
control codes Inducedrepresentation, in mathematics, an operation for passing from a representation of a subgroup to a representation of the group itself...
the basic representation is called an induced discrete series representation. Any irreducible tempered representation is a basic representation, and conversely...
representation, then direct calculation using (G5) shows that the inducedrepresentation on End(V) is a proper representation, i.e. a representation without...
of the induced character θG. This induced character vanishes on all elements of G which are not conjugate to any element of H. Since the induced character...
discrete spectrum/continuous spectrum, or discrete series representation/inducedrepresentation distinction typical in different parts of spectral theory...
closed subgroup. In line with the concepts of regular representation and inducedrepresentation, G acts on functions on G/H. If however Haar measures...
kernel. If S is any non-trivial irreducible representation of K, then the corresponding inducedrepresentation of G is also irreducible. These give the irreducible...
Artin's theorem on induced characters states that a character on a finite group is a rational linear combination of characters induced from cyclic subgroups...
function Representation theory of finite groups Modular representation theory Frobenius reciprocity Restricted representationInducedrepresentation Peter–Weyl...
the other conjectures presented so far. It is of the nature of an inducedrepresentation construction—what in the more traditional theory of automorphic...
category theory, too. Frobenius reciprocity in the representation theory of groups: see inducedrepresentation. This example foreshadowed the general theory...
{\displaystyle \Delta } and representation ρ {\displaystyle \rho } behaves as a highest-weight vector in an inducedrepresentation of the conformal group from...
every year from 2004 to 2009. The Human-Induced Earthquake Database (HiQuake) documents all reported cases of induced seismicity proposed on scientific grounds...
group.) The induced representations of such ρ make up the principal series. The spherical principal series consists of representations induced from 1-dimensional...
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