Quantum matrix ball: the Bergman kernel
Quantum Algebra
2007-05-23 v2 Complex Variables
Functional Analysis
Abstract
In our preprint q-alg/9703005 q-analogues of bounded symmetric domains were defined to be homogeneous spaces of the associated quantum groups. The investigation of a simplest among those domains, the quantum matrix ball, was started in math.QA/9803110. This work presents a construction of q-analogues for Hardy-Bergman spaces of 'functions in those balls', together with an explicit form of the Bergman kernel. Besides that, two auxiliary results are also established: a boundedness of matrix balls is proved, and de Rham complexes of differential forms with finite coefficients in those balls are constructed.
Cite
@article{arxiv.math/9909036,
title = {Quantum matrix ball: the Bergman kernel},
author = {D. Shklyarov and S. Sinel'shchikov and L. Vaksman},
journal= {arXiv preprint arXiv:math/9909036},
year = {2007}
}
Comments
LaTeX2e, 28 pages, [email protected], [email protected]