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

2010
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Symmetry, Integrability and Geometry: Methods and Applications
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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.

doi:10.3842/sigma.2010.010
fatcat:iintaf77rvf2bm4aholjus6bpy