Function Theory on a q-Analog of Complex Hyperbolic Space

Details Function Theory on a q-Analog of Complex Hyperbolic Space Function Theory on a q-Analog of Complex Hyperbolic Space

2010-09-30

arxiv.org/abs/1009.6063v2

Mathematics

Quantum Algebra

21 pages

Scientific paper

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 $U_q \mathfrak{su}_{n,m}$-modules related to this cone, and obtain the necessary conditions for those modules to be equivalent.

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