Geodesic
Geometric realizations for some series of representations of the quantum group $SU_{2,2}$
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 1, pp. 90-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper solves the problem of analytic continuation for the holomorphic discrete series of representations for the quantum group $SU(2,2)$. In particular, a new realization of the ladder representation of this group is produced. Besides, $q$-analogues are constructed for the Shilov boundary of the unit ball in the space of complex $2\times 2$ matrices and the principal degenerate series representations of $SU(2,2)$ associated to that boundary. A possibility is discussed of transferring some well known geometric constructions of the representation theory to the quantum case: the Penrose transform, the Beilinson–Bernstein approach to the construction of Harish–Chandra modules (for the case of the principal nondegenerate series). 
@article{JMAG_2001_8_1_a5,
     author = {D. Shklyarov and S. Sinel'shchikov and L. Vaksman},
     title = {Geometric realizations for some series of representations of the quantum group~$SU_{2,2}$},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {90--110},
     year = {2001},
     volume = {8},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_1_a5/}
}
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D. Shklyarov; S. Sinel'shchikov; L. Vaksman. Geometric realizations for some series of representations of the quantum group $SU_{2,2}$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 1, pp. 90-110. http://geodesic.mathdoc.fr/item/JMAG_2001_8_1_a5/