A NOTE ON THE HARMONIC REPRESENTATION OF SU(p,q)

Benjamin Cahen

doi:nihmj/1687775160

Abstract

We derive an explicit formula for the harmonic representation of $SU(p,q)$ in the Fock space from the holomorphic representations of the semi-direct product of the $(2p+2q+1)$ -dimensional Heisenberg group by $SU(p,q)$ .

Acknowledgements

I would like to thank the anonymous referee for carefully reading the manuscript and suggesting many improvements to it.

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Benjamin Cahen. "A NOTE ON THE HARMONIC REPRESENTATION OF $SU(p,q)$ ." Nihonkai Math. J. 33 (2) 61 - 79, 2022.

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Received: 12 July 2022; Revised: 4 April 2023; Published: 2022

First available in Project Euclid: 11 July 2023

MathSciNet: MR4622662

zbMATH: 07721315

Subjects:

Primary: 22E46

Secondary: 46E22 , 47B32

Keywords: harmonic representation , Heisenberg group , holomorphic representation , oscillator representation , ‎reproducing kernel Hilbert ‎space , unitary group , unitary representation

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Acknowledgements

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