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...ем. сб., 13(55):2–3 (1943), 301–316], (I. Gelfand, D. Raikov, "Irreducible unitary representations of locally bicompact groups", Recueil Mathématique. N.S., 1 ...rojecteuclid.org/download/pdf_1/euclid.ojm/1200685627 Yoshizawa, Hisaaki. "Unitary representations of locally compact groups. Reproduction of Gelfand–Raikov's ...

...<math>(\mathfrak{g},K)</math>-module, then its Harish-Chandra module is a representation with desirable factorization properties. ...p and ''K'' a compact [[subgroup]] of ''G''. If <math>(\pi,V)</math> is a representation of ''G'', then the ''Harish-Chandra module'' of <math>\pi</math> is the sub ...

...] of a [[C*-algebra]], or to the factor for a [[von Neumann algebra]]: the representation <math>\pi </math> of G is isotypical iff <math>\pi(G)^{''} </math> is a fac ...quasi-equivalent or disjoint (in analogy with the fact that [[irreducible representation]]s are either unitarily equivalent or disjoint). ...

...ion|representation]] of a [[group (mathematics)|group]] or a [[Lie algebra representation|Lie algebra]] on a [[symplectic vector space]] (''V'', ''ω'') which preserv where '''F''' is the [[field (mathematics)|field]] of scalars. A representation of a group ''G'' preserves ''ω'' if ...

...orlink=Alexandre Kirillov|last=Kirillov|year=1963}}, is a realization of a representation of ''GL''₂ over a [[local field]] on a space of functions on the and π is an [[irreducible representation]] of ''G''('''F'''), then the Kirillov model for π is ...

...rish-Chandra showed that the study of [[Unitary representation|irreducible unitary representations]] of a real reductive [[Lie group]], ''G'', could be reduce ...[[Lie algebra representation]] of <math>\mathfrak{g}</math> and a [[group representation]] of ''K'' (without regard to the [[topological space|topology]] of ''K'') ...

...ame="m157">{{cite report |title=Lectures on RCFT (Rational Conformal Field Theory) |last1=Moore |first1=G |last2=Seiberg |first2=N |date=1989-09-01 |doi=10.2 ...[Reshetikhin–Turaev invariant|Reshetikhin–Turaev topological quantum field theory]] associated to <math>\mathcal{C}</math>.<ref name=":113">{{Cite book |last ...

...s of the American Mathematical Society 150.2 (1970): 611-618.</ref> is a [[unitary transformation]] that maps a [[Schwartz function]] on the real line to a s The '''Weil–Brezin map''' <math>W: L^2(\mathbb R) \to H_1</math> is the unitary transformation given by ...

...ials. The [[representation theory]] of these groups leads to [[irreducible representation]]s, which for SO(3) gives the angular momentum ket vectors of the system. ..., and including these in the symmetry group leads to groups including both unitary and antiunitary operators. ...

{{Short description|Braid group representation}} ...ion is the [[Burau representation]] and the second is the Lawrence–Krammer representation. ...

...Swiss mathematician [[Michel Plancherel]] for his work in [[representation theory]]. ...ath>G</math> be a [[finite group]], we denote the set of its [[irreducible representation]]s by <math>G^\wedge</math>. The corresponding '''Plancherel measure''' ove ...

...named by {{harvtxt|Collins|2003}}, who evaluated them explicitly for the [[unitary group]]. ==Unitary groups== ...

...form]]s. Harish-Chandra used Eisenstein integrals to decompose the regular representation of a semisimple Lie group into representations induced from parabolic subgr *τ is a finite-dimensional unitary double representation of ''K'' ...

{{short description|In mathematics, representation of a reductive algebraic group}} ...r the group SL₂('''R''') some of the functions involved in the representation are [[Whittaker function]]s. ...

In [[mathematics]], and more specifically in the theory of [[C*-algebra]]s, the '''noncommutative tori''' ''A''_θ, also k ...] <math>S^1 \subset \mathbb{C}</math>, generated by two [[unitary operator|unitary]] operators <math>U, V</math> defined as<blockquote><math>\begin{align} ...

...on <math>f : G \to \Complex</math> at a [[representation of a finite group|representation]] <math>\varrho : G \to \mathrm{GL}_{d_\varrho}(\Complex)</math> of <math>G For each representation <math>\varrho</math> of <math>G</math>, <math>\widehat{f}(\varrho)</math> i ...

{{Short description|Type of symmetry in quantum theory}} ==In field theory== ...

| field = [[Representation theory]] ...central critical L-values, and restriction problems in the representation theory of classical groups | mr=3202556 | year=2012 | journal=[[Astérisque]] | isb ...

{{Lie groups|Representation}} In mathematics, the finite-dimensional [[representation theory|representations]] of the complex [[classical Lie groups]] ...

...lements <math>g,h</math> of <math>G</math> there is an irreducible unitary representation <math>\rho</math> with <math>\rho (g) \neq \rho (h)</math>.<ref name="NCAT" He also worked on [[probability theory]], for example in 1938 he proved an equivalent of the [[Cramér's decomposit ...