Geodesic
Decomposition of boundary representations on the Lobachevsky plane associated with linear bundles
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 128, pp. 368-375 Cet article a éte moissonné depuis la source Math-Net.Ru

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Earlier we described canonical (labelled by $\lambda\in \Bbb C$) and accompanying boundary representations of the group $G={\rm {SU}} \, (1,1)$ on the Lobachevsky plane $D$ in sections of linear bundles and decomposed canonical representations into irreducible ones. Now we decompose representations acting on distributions concentrated at the boundary of $D$. In the generic case $2\lambda\notin \Bbb N$ they are diagonalizable, in the exceptional case Jordan blocks appear.
Keywords: Lobachevsky plane; canonical representations; distributions; boundary representations; Poisson transforms. 
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     title = {Decomposition of boundary representations on the {Lobachevsky} plane associated with linear bundles},
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L. I. Grosheva. Decomposition of boundary representations on the Lobachevsky plane associated with linear bundles. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 128, pp. 368-375. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_128_a2/

[1] V. F. Molchanov, L. I. Grosheva, “Canonical and boundary representations on the Lobachevsky plane”, Acta Appl. Math., 73 (2002), 59–77 | DOI | MR | Zbl

[2] L. I. Grosheva, “Canonical representations on sections of linear bundles on the Lobachevsky plane”, Tambov University Reports. Series: Natural and Technical Sciences, 12:4 (2007), 436–438

[3] L. I. Grosheva, “Canonical and boundary representations on the Lobachevsky plane associated with linear bundles”, Tambov University Reports. Series: Natural and Technical Sciences, 22:6 (2017), 1218–1228 | DOI

[4] L. I. Grosheva, “Decomposition of canonical representations on the Lobachevsky plane associated with linear bundles”, Tambov University Reports. Series: Natural and Technical Sciences, 23:122 (2018), 113–124 | DOI