Function theory on a q-analog of complex hyperbolic space

被引：1
|
作者：
Bershtein, O. [1 ]
Sinel'shchikov, S. [1 ]
机构：
[1] Natl Acad Sci Ukraine, B Verkin Inst Low Temp Phys & Engn, Div Math, UA-61103 Kharkov, Ukraine
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2012年 / 62卷 / 05期
关键词：
Quantum groups; Non-commutative complex analysis; Hyperbolic spaces; Geometric realizations of representations of real Lie groups;
D O I：
10.1016/j.geomphys.2011.07.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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)su(n,m)-modules related to this cone, and obtain the necessary conditions for those modules to be equivalent. (C) 2011 Elsevier B.V. All rights reserved.
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页码：1323 / 1337
页数：15
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