Quantum matrix ball: the weighted Bergman kernels

arXivmath/9809038MaRDI QIDQ6501011

Sergey D. Sinelshchikov, D. L. Shklyarov, L. L. Vaksman

Abstract: 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.

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) General mathematical topics and methods in quantum theory (81Q99)

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