Journal of Nonlinear Mathematical Physics

Volume 17, Issue 2, June 2010, Pages 137 - 144

A Weil Representation of sp(4) Realized by Differential Operators in the Space of Smooth Functions on S2 × S1

Authors
H. Fakhri
Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran
Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5531, Tehran, Iran, hfakhri@tabrizu.ac.ir
Received 5 September 2008, Accepted 4 December 2009, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925110000660How to use a DOI?
Keywords
Lie groups, Lie algebra, Weil representation
Abstract

In the space of complex-valued smooth functions on S2 × S1, we explicitly realize a Weil representation of the real Lie algebra sp(4) by means of differential generators. This representation is a rare example of highest weight irreducible representation of sp(4) all whose weight spaces are 1-dimensional. We also show how this space splits into the direct sum of irreducible sl(2)-submodules. Selected applications: complete classification of yrast-band energies in even-even nuclei, the dynamical symmetry in some collective models of nuclear structure, the mapping methods for simplifying initial problem Hamiltonians.

Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - 2
Pages
137 - 144
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925110000660How to use a DOI?
Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - H. Fakhri
PY  - 2021
DA  - 2021/01
TI  - A Weil Representation of sp(4) Realized by Differential Operators in the Space of Smooth Functions on S² × S¹
JO  - Journal of Nonlinear Mathematical Physics
SP  - 137
EP  - 144
VL  - 17
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000660
DO  - https://doi.org/10.1142/S1402925110000660
ID  - Fakhri2021
ER  -