2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60796This work produces a q-analogue of the Cauchi-Szegö integral representation that retrieves a holomorphic function in the matrix ball from its values on the Shilov boundary. Besides that, the Shilov boundary of the quantum matrix ball is described and the U_q su(m,n)-covariance of the U_q s(u(m)x u(n))-invariant integral on this boundary is established. The latter result allows one to obtain a q-analogue for the principal degenerate series of unitary representations related to the Shilov boundary of the matrix ball.LaTeX 2e, 15 pages, vaksman@ilt.kharkov.uaQuantum AlgebraComplex VariablesFunctional Analysis81R50 (Primary) 81Q99 (Secondary)text