Geodesic
Guantum matrix ball: the Cauchy–Szegö kernel and the Shilov boundary
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 4, pp. 366-384 Cet article a éte moissonné depuis la source Math-Net.Ru

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This work produces a q-analogue of the Cauchy–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 $U_q\mathfrak{su}_{m,n}$-covariance of the $U_q\mathfrak{s}(\mathfrak{u}_m \times \mathfrak{u}_n)$-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. 
@article{JMAG_2001_8_4_a1,
     author = {L. Vaksman},
     title = {Guantum matrix ball: the {Cauchy{\textendash}Szeg\"o} kernel and the {Shilov} boundary},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {366--384},
     year = {2001},
     volume = {8},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_4_a1/}
}
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L. Vaksman. Guantum matrix ball: the Cauchy–Szegö kernel and the Shilov boundary. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 4, pp. 366-384. http://geodesic.mathdoc.fr/item/JMAG_2001_8_4_a1/