Representation theory of the nonlinear SU (2) algebra

M. Roček

doi:10.1016/0370-2693(91)90265-R

Representation theory of the nonlinear SU (2) algebra

M. Roček

Institute for Theoretical Physics

Research output: Contribution to journal › Article › peer-review

147 Scopus citations

Abstract

A deformed quadratic Casimir operator is constructed for nonlinearly deformed SU (2) algebras, and the representation theory is investigated. Different deformations give rise to different kinds of finite dimensional unitary representations, including periodic representations as in quantum groups, as well as "extra", "truncated" and "missing" representations. Remarkably, certain deformations allow only finite numbers of unitary representations ("maximum spin" representations). A free oscillator representation is given.

Original language	English
Pages (from-to)	554-557
Number of pages	4
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	255
Issue number	4
DOIs	https://doi.org/10.1016/0370-2693(91)90265-R
State	Published - Feb 21 1991

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title = "Representation theory of the nonlinear SU (2) algebra",

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N2 - A deformed quadratic Casimir operator is constructed for nonlinearly deformed SU (2) algebras, and the representation theory is investigated. Different deformations give rise to different kinds of finite dimensional unitary representations, including periodic representations as in quantum groups, as well as "extra", "truncated" and "missing" representations. Remarkably, certain deformations allow only finite numbers of unitary representations ("maximum spin" representations). A free oscillator representation is given.

AB - A deformed quadratic Casimir operator is constructed for nonlinearly deformed SU (2) algebras, and the representation theory is investigated. Different deformations give rise to different kinds of finite dimensional unitary representations, including periodic representations as in quantum groups, as well as "extra", "truncated" and "missing" representations. Remarkably, certain deformations allow only finite numbers of unitary representations ("maximum spin" representations). A free oscillator representation is given.

UR - https://www.scopus.com/pages/publications/0038161305

U2 - 10.1016/0370-2693(91)90265-R

DO - 10.1016/0370-2693(91)90265-R

M3 - Article

AN - SCOPUS:0038161305

SN - 0370-2693

VL - 255

SP - 554

EP - 557

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 4

ER -

Representation theory of the nonlinear SU (2) algebra

Abstract

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