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arXiv · 0912.5403

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

R. M. Asherova·Č. Burdík·M. Havlíček·Yu. F. Smirnov·V. N. Tolstoy
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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.

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BibTeXRIS

R. M. Asherova, Č. Burdík, M. Havlíček, Yu. F. Smirnov, V. N. Tolstoy. 2010-01-26. q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1)). https://doi.org/10.3842/sigma.2010.010

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