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

Symmetry Integrability and Geometry-Methods and Applications

article

Raisa M. Asherova¹  Čestmír Burdík²  Miloslav Havlíček²  Yuri F. Smirnov¹  Valeriy N. Tolstoy¹ 

[1] Institute of Nuclear Physics, Moscow State University;Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague;Deceased

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

DOI  :  10.3842/SIGMA.2010.010

来源: National Academy of Science of Ukraine

【 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】

Unknown