Abstract
We classify all irreducible coherent state representations of the holomorphic automorphism group of the tube domain over the dual of the Vinberg cone.
Dedicated to the memory of Professor Takaaki Nomura.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K. Arashi, Holomorphic multiplier representations for bounded homogeneous domains. J. Lie Theory 30, 1091–1116 (2020)
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)
S.-S. Chen, Bounded holomorphic functions in Siegel domains. Proc. Am. Math. Soc. 40, 539–542 (1973)
I.G. Dotti, Rigidity of invariant complex structures. Trans. Am. Math. Soc. 338, 159–172 (1993)
L. Geatti, Holomorphic automorphisms of some tube domains over nonselfadjoint cones. Rend. Circ. Mat. Palermo (2), 36, 281–331 (1987)
S.G. Gindikin, I.I. PjateckiÄ-Å apiro, 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
H. Ishi, Unitary holomorphic multiplier representations over a homogeneous bounded domain. Adv. Pure Appl. Math. 2, 405–419 (2011)
H. Ishi, K. Koufany, The compression semigroup of the dual Vinberg cone (2020), 12 p.
S. Kobayashi, Irreducibility of certain unitary representations. J. Math. Soc. Jpn. 20, 638–642 (1968)
R.A. Kunze, On the irreducibility of certain multiplier representations. Bull. Am. Math. Soc. 68, 93–94 (1962)
W. Lisiecki, Kaehler coherent state orbits for representations of semisimple Lie groups. Ann. Inst. H. Poincaré Phys. Théor. 53, 245–258 (1990)
W. Lisiecki, A classification of coherent state representations of unimodular Lie groups. Bull. Am. Math. Soc. (N.S.), 25, 37–43 (1991)
W. Lisiecki, Coherent state representations. a survey. Rep. Math. Phys. 35, 327–358 (1995)
K.-H. Neeb, Holomorphy and Convexity in Lie Theory. De Gruyter Expositions in Mathematics, vol. 28 (Walter de Gruyter, Berlin, 2000)
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)
J. Rosenberg, M. Vergne, Harmonically induced representations of solvable Lie groups. J. Funct. Anal. 62, 8–37 (1985)
J.A. Tirao, J.A. Wolf, Homogeneous holomorphic vector bundles. Indiana Univ. Math. J. 20, 15–31 (1970/71)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Arashi, K. (2021). Coherent State Representations of the Holomorphic Automorphism Group of the Tube Domain over the Dual of the Vinberg Cone. In: Baklouti, A., Ishi, H. (eds) Geometric and Harmonic Analysis on Homogeneous Spaces and Applications . TJC 2019. Springer Proceedings in Mathematics & Statistics, vol 366. Springer, Cham. https://doi.org/10.1007/978-3-030-78346-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-78346-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-78345-7
Online ISBN: 978-3-030-78346-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)