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

Symmetry, Integrability and Geometry: Methods and Applications

关键词: quantum algebra;    extremal projector;    reduction algebra;    Shapovalov form;    noncompact quantum algebra;    discrete series of representations;    Gelfand-Graev basis;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

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