Translator Disclaimer
September 2017 The moment map on symplectic vector space and oscillator representation
Takashi Hashimoto
Kyoto J. Math. 57(3): 553-583 (September 2017). DOI: 10.1215/21562261-2017-0006

Abstract

Let G denote Sp(n,R), U(p,q), or O(2n). The main aim of this article is to show that the canonical quantization of the moment map on a symplectic G-vector space (W,ω) naturally gives rise to the oscillator (or Segal–Shale–Weil) representation of g:=Lie(G)C. More precisely, after taking a complex Lagrangian subspace V of the complexification of W, we assign an element of the Weyl algebra for V to μ,X for each Xg, which we denote by μˆ,X. Then we show that the map Xiμˆ,X gives a representation of g. With a suitable choice of V in each case, the representation coincides with the oscillator representation of g.

Citation

Download Citation

Takashi Hashimoto. "The moment map on symplectic vector space and oscillator representation." Kyoto J. Math. 57 (3) 553 - 583, September 2017. https://doi.org/10.1215/21562261-2017-0006

Information

Received: 11 May 2015; Revised: 10 November 2015; Accepted: 21 April 2016; Published: September 2017
First available in Project Euclid: 3 May 2017

zbMATH: 1373.22023
MathSciNet: MR3685055
Digital Object Identifier: 10.1215/21562261-2017-0006

Subjects:
Primary: 22E46
Secondary: 17B20, 81S10

Rights: Copyright © 2017 Kyoto University

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.57 • No. 3 • September 2017
Back to Top