Function Theory on a q-Analog of Complex Hyperbolic Space

2010/09/30 by Olga Bershtein, O. Bershtein, Bershtein, O. +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.CV #math.QA #math.RT #msc:17B37 #msc:20G42

paper · pdf · doi:10.48550/arxiv.1009.6063

21 pages

arxiv created 2011/08/16 · arxiv updated 2011/08/18

Abstract

This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated quantum isotropic cone. Also we establish principal series of U_q \mathfraksu_n,m-modules related to this cone, and obtain the necessary conditions for those modules to be equivalent.

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