q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1))

Details q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1)) q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1))

2009-12-30

arxiv.org/abs/0912.5403v2

SIGMA 6 (2010), 010, 13 pages

Mathematics

Quantum Algebra

Invited talk given by V.N.T. at XVIII International Colloquium "Integrable Systems and Quantum Symmetries", June 18--20, 2009,

Scientific paper

10.3842/SIGMA.2010.010

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.

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