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...t group#Representation theory of a connected compact Lie group|irreducible representations]] of a connected compact [[Lie group]] <math>K</math>.<ref name="12.6">{{ha ...lts is in the precise notion of "integral" in the definition of a dominant integral element. If <math>K</math> is simply connected, this distinction disappears ...

.... Feichtinger and K. Gröchenig. "Banach spaces related to integrable group representations and their atomic decompositions, II" Monatsh. Math. 108(2-3):129–148, 1989. ...f * V_g g</math>. By [[discretization]] of this continuous [[convolution]] integral it can be shown that by sufficiently dense sampling in phase space the corr ...

== Integral representations == ...th> is defined for <math>x \in \mathbb{R}^d \setminus \{0\} </math> by the integral formula <ref>{{cite book|last1=Stein|first1=Elias|title=Singular integrals ...

Where the new parameter <math>w</math> defines the integral bound of the '''upper-incomplete form''' and '''lower-incomplete form''' of ==Integral representations== ...

==Alternative Representations== ===Integral Representations=== ...

...ic ''L''-functions]]. Some authors reserve the term for a special type of integral representation, namely those that involve an [[Eisenstein series]]. It has ...of [[general linear group|GL]](2) with itself. Like Riemann, they used an integral of modular forms, but one of a different type: they integrated the product ...

==Alternative Representations== ===Integral Representation=== ...

...1= Blagouchine|first1= Iaroslav V.|title= Three notes on Ser's and Hasse's representations for the zeta-functions |journal= INTEGERS: The Electronic Journal of Combin ==Integral representations== ...

...als to decompose the regular representation of a semisimple Lie group into representations induced from parabolic subgroups.<ref>{{harvtxt|Harish-Chandra|1975}}; {{ha ...{harvtxt|Harish-Chandra|1970|loc=section 10}}</ref> defined the Eisenstein integral by ...

== Projective representations == ...roup]]. Projective representations of ''G'' correspond naturally to linear representations of the covering group of ''G''. ...

...it gives a way to parametrize (or classify) irreducible finite-dimensional representations of a semisimple Lie algebra, the result known as the [[theorem of the highe ...ng point for the general theory of [[representation of a compact Lie group|representations of connected compact Lie groups]]. ...

...f>{{cite book|chapter=''SD Herman's Contribution to the Theory of Integral Representations of Finite Groups'' by Alexander I. Lichtman|title=Representation Theory, Gr ...le representations of an algebra with an infinite number of indecomposable representations", Izv. Akad. Nauk SSSR Ser. Mat., 32:6 (1968), 1275–1282; Math. USSR-Izv., ...

{{short description|Generalization of the Cauchy integral formula}} ..., the '''Bochner–Martinelli formula''' is a generalization of the [[Cauchy integral formula]] to functions of [[several complex variables]], introduced by {{ha ...

One way to view these functions is as representations of the "parent" function that takes a point of the manifold as an argument The integral of <math>f</math> over the region <math>D</math> is{{cn|date=August 2022}} ...

...en in Polynombereichen'' (Representations of finite groups in polynomial [[integral domain]]s) was written under the supervision of [[Hermann Boerner]].<ref>{{ ...most developments which followed in the study of finite groups of units of integral group rings.<ref name=bio/> ...

...k integral''' in contrast to the [[Bochner integral]], which is the strong integral. ...}}''' of <math>f</math> on <math>A.</math> Common notations for the Pettis integral <math>e_A</math> include ...

...enberg|Yuzhakov|1983|p=38}}.</ref> however, when {{math|''n'' > 1}}, its [[integral kernel]] is not obtainable by simple differentiation of the [[Bochner–Marti ==The Andreotti–Norguet integral representation formula== ...

...cite journal|doi=10.1090/S0002-9939-07-09124-1|title=A categorification of integral Specht modules|year=2007|last1=Khovanov|first1=Mikhail|last2=Mazorchuk|firs * {{cite journal|doi=10.1090/S0002-9939-09-09857-8|title=On the irreducible representations of a finite semigroup|year=2009|last1=Ganyushkin|first1=Olexandr|last2=Mazo ...

integral can be described by four indices, that is the indices of the four basis fun It is customary to denote these indices as p,q,r and s and the integral as (pq|rs). Assuming that ...

...id group]]s. It fits into a family of representations called the Lawrence representations. The first Lawrence representation is the [[Burau representation]] and the ...sics)|configuration space]] <math>C_2 P_n</math>. Specifically, the first integral [[Homology (mathematics)|homology group]] of <math>C_2 P_n</math> is isomor ...