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Coherent state representations of the holomorphic automorphism group of the tube domain over the dual of the Vinberg cone. (English) Zbl 1487.32113

Baklouti, Ali (ed.) et al., Geometric and harmonic analysis on homogeneous spaces and applications. TJC 2019, Djerba, Selected papers based on the presentations at the 6th Tunisian-Japanese conference. In honor of Professor Takaaki Nomura. Tunisia, December 15–19, 2019. Cham: Springer. Springer Proc. Math. Stat. 366, 7-23 (2021).
Summary: We classify all irreducible coherent state representations of the holomorphic automorphism group of the tube domain over the dual of the Vinberg cone.
For the entire collection see [Zbl 1477.43001].

MSC:

32M05 Complex Lie groups, group actions on complex spaces
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References:

[1] Arashi, K., Holomorphic multiplier representations for bounded homogeneous domains, J. Lie Theory, 30, 1091-1116 (2020) · Zbl 1462.32026
[2] P. Bernat, N. Conze, M. Duflo, M. Lévy-Nahas, M. Raïs, P. Renouard, M. Vergne, Représentations Des Groupes de Lie Résolubles. Monographies de La Société Mathématique de France, vol. 4 (Dunod, Paris, 1972) · Zbl 0248.22012
[3] Chen, S-S, Bounded holomorphic functions in Siegel domains, Proc. Am. Math. Soc., 40, 539-542 (1973) · Zbl 0277.32001 · doi:10.1090/S0002-9939-1973-0322211-X
[4] Dotti, IG, Rigidity of invariant complex structures, Trans. Am. Math. Soc., 338, 159-172 (1993) · Zbl 0780.32004 · doi:10.1090/S0002-9947-1993-1100696-6
[5] L. Geatti, Holomorphic automorphisms of some tube domains over nonselfadjoint cones. Rend. Circ. Mat. Palermo (2), 36, 281-331 (1987) · Zbl 0652.32021
[6] S.G. Gindikin, I.I. Pjateckiĭ-Šapiro, È.B. Vinberg, Homogeneous Kähler manifolds, in Geometry of Homogeneous Bounded Domains, ed. by E. Vesentini. C.I.M.E. Summer Schools, vol. 45 (Springer, Berlin, 1968), pp. 1-87 · Zbl 0183.35401
[7] Ishi, H., Unitary holomorphic multiplier representations over a homogeneous bounded domain, Adv. Pure Appl. Math., 2, 405-419 (2011) · Zbl 1228.32023 · doi:10.1515/apam.2010.037
[8] H. Ishi, K. Koufany, The compression semigroup of the dual Vinberg cone (2020), 12 p.
[9] Kobayashi, S., Irreducibility of certain unitary representations, J. Math. Soc. Jpn., 20, 638-642 (1968) · Zbl 0165.40504 · doi:10.2969/jmsj/02040638
[10] Kunze, RA, On the irreducibility of certain multiplier representations, Bull. Am. Math. Soc., 68, 93-94 (1962) · Zbl 0107.28604 · doi:10.1090/S0002-9904-1962-10735-6
[11] Lisiecki, W., Kaehler coherent state orbits for representations of semisimple Lie groups, Ann. Inst. H. Poincaré Phys. Théor., 53, 245-258 (1990) · Zbl 0724.22013
[12] W. Lisiecki, A classification of coherent state representations of unimodular Lie groups. Bull. Am. Math. Soc. (N.S.), 25, 37-43 (1991) · Zbl 0736.22008
[13] W. Lisiecki, Coherent state representations. a survey. Rep. Math. Phys. 35, 327-358 (1995) · Zbl 0883.22011
[14] K.-H. Neeb, Holomorphy and Convexity in Lie Theory. De Gruyter Expositions in Mathematics, vol. 28 (Walter de Gruyter, Berlin, 2000)
[15] A.L. Onishchik, È.B. Vinberg, Lie Groups and Lie Algebras, III: Structure of Lie Groups and Lie Algebras. Encyclopaedia of Mathematical Sciences, vol. 41 (Springer, Berlin, 1994) · Zbl 0797.22001
[16] Rosenberg, J.; Vergne, M., Harmonically induced representations of solvable Lie groups, J. Funct. Anal., 62, 8-37 (1985) · Zbl 0602.22008 · doi:10.1016/0022-1236(85)90017-5
[17] J.A. Tirao, J.A. Wolf, Homogeneous holomorphic vector bundles. Indiana Univ. Math. J. 20, 15-31 (1970/71) · Zbl 0197.49801
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