q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1))
Quantum Algebra
2010-01-26 v2 High Energy Physics - Theory
Representation Theory
Abstract
For the quantum algebra U_q(gl(n+1)) in its reduction on the subalgebra U_q(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction Z-algebra Z_q(gl(n+1),gl(n)) is given in terms of the generators and their defining relations. Using this Z-algebra we describe Hermitian irreducible representations of a discrete series for the noncompact quantum algebra U_q(u(n,1)) which is a real form of U_q(gl(n+1)), namely, an orthonormal Gelfand-Graev basis is constructed in an explicit form.
Keywords
Cite
@article{arxiv.0912.5403,
title = {q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1))},
author = {R. M. Asherova and Č. Burdík and M. Havlíček and Yu. F. Smirnov and V. N. Tolstoy},
journal= {arXiv preprint arXiv:0912.5403},
year = {2010}
}
Comments
Invited talk given by V.N.T. at XVIII International Colloquium "Integrable Systems and Quantum Symmetries", June 18--20, 2009, Prague, Czech Republic