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An Integral Transform and Unitary Highest Weight Modules
Author(s) -
Lorch John D.
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012491
Subject(s) - mathematics , unitary state , inverse , fock space , realization (probability) , pure mathematics , bounded function , unitary representation , integral transform , representation (politics) , algebra over a field , discrete mathematics , mathematical analysis , geometry , lie group , statistics , physics , quantum mechanics , politics , political science , law
The unitary highest weight modules for G = U(1, q ), which occur as irreducible subrepresentations of the oscillator representation on a Fock space F, can each be realized on a space of polynomial‐valued functions over the bounded realization B q of G / K . This is achieved via an integral transform constructed by L. Mantini. A decomposition of these representations into K ‐types is given, including an explicit description of how Mantini's transform behaves on K ‐types. An inverse is produced for the transform, thus giving unitary structures for the geometric realizations of the unitary highest‐weight modules over G / K . 1991 Mathematics Subject Classification : 22E45, 22E70.
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