Quantum matrix ball: the weighted Bergman kernels

Details Quantum matrix ball: the weighted Bergman kernels Quantum matrix ball: the weighted Bergman kernels

1998-09-08

arxiv.org/abs/math/9809038v2

Mathematics

Quantum Algebra

LaTeX 2.09, 5 pages, vaksman@ilt.kharkov.ua, sinelshchikov@ilt.kharkov.ua

Scientific paper

We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a positive $U_q\frak{su}_{nm}$-invariant integral (see math.QA/9803110) is used to define q-analogues for weighted Bergman spaces. The orthogonal projections onto these spaces are integral operators; this work presents an explicit formula for their kernels.

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