Discrete series of unitary irreducible representations of the U{sub q}(u(3, 1)) and U{sub q}(u(n, 1)) noncompact quantum algebras

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778811060275· OSTI ID:22043915

Smirnov, Yu F

The structure of all discrete series of unitary irreducible representations of the U{sub q}(u(3, 1)) and U{sub q}(u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g Prime ){sub q}. The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U{sub q}(u(n, 1)) Superset-Of-Or-Equal-To U{sub q}(u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) Superset-Of-Or-Equal-To u(n) classical algebra.

• OSTI ID: 22043915
• Journal Information: Physics of Atomic Nuclei, Vol. 74, Issue 6; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
IRREDUCIBLE REPRESENTATIONS
MANY-DIMENSIONAL CALCULATIONS
PROJECTION OPERATORS
QUANTUM FIELD THEORY
SPACE
U GROUPS
UNITARITY