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
- 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/).
Cite this article
TY - JOUR AU - H. Fakhri PY - 2021 DA - 2021/01/07 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 - 10.1142/S1402925110000660 ID - Fakhri2021 ER -