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Oscillator representation

In mathematics, the oscillator representation is a projective unitary representation of the symplectic group, first investigated by Irving Segal, David Shale, and André Weil. A natural extension of the representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously…

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Overview

Historical overview

Semigroups in SL(2,C)

Commutation relations of Heisenberg and Weyl

Fourier transform

Stone–von Neumann theorem

Oscillator representation of SL(2,R)

Maslov index

Holomorphic Fock space

Disk model

Harmonic oscillator and Hermite functions

Sobolev spaces

Smooth vectors

Analytic vectors

Oscillator semigroup

Weyl calculus

Applications and generalizations

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Oscillator representation

Nodes165
Edges164
Triples198
Avg. degree1.99
Density0.012121
Components1

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Oscillator representation

Top relations

related to References · 161
Oscillator representation → Academic Press, Academic PressLang, Acta Mathematica, Addison-Wesley, Advanced, Algebra, American Mathematical Society, Analysis, Analytic, Angewandte Mathematik, Annals, Applications, Applied Mathematics, Baez, BF02391012Wiener, Bibcode, Birkhäuser, Bombay, Breach, Cambridge University Press
related to Theory in infinite dimensions · 21
Oscillator representation → At, Cn, David Shale, Fock, Graeme Segal, Hilbert, Irving Segal, Kac, L2, Lie, LU, Moody, Neretin, Olshanskii, Only, Segal, Sk, SU, The, Virasoro
related to Theory in higher dimensions · 9
Oscillator representation → Folland, For, L2, Let, Rn, Schwartz, SL, Sp, The
related to Theory for finite abelian groups · 5
Oscillator representation → Let, Neumann, Stone, Thus, Weil
is a · 2
Oscillator representation → projective unitary representation of the symplectic group, unitary representation of a double cover of SU

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Important terminology

displaystyle operators representation group mathcal semigroup unitary operator follows functions given space defined l2 oscillator sl metaplectic lies formula form

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Oscillator representationis aprojective unitary representation of the symplectic group0.90text
Oscillator representationis aunitary representation of a double cover of SU0.90text
Oscillator representationrelated to ReferencesLock-green0.60section
Oscillator representationrelated to ReferencesLock-gray-alt-20.60section
Oscillator representationrelated to ReferencesLock-red-alt-20.60section
Oscillator representationrelated to ReferencesWikisource-logo0.60section
Oscillator representationrelated to ReferencesBaez0.60section
Oscillator representationrelated to ReferencesSegal0.60section
Oscillator representationrelated to ReferencesZhou0.60section
Oscillator representationrelated to ReferencesKon0.60section
Oscillator representationrelated to ReferencesMark0.60section
Oscillator representationrelated to ReferencesIntroduction0.60section

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