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Title: Stratonovich-Weyl correspondence for the Jacobi group (English)
Author: Cahen, Benjamin
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388
Volume: 22
Issue: 1
Year: 2014
Pages: 31-48
Summary lang: English
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Category: math
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Summary: We construct and study a Stratonovich-Weyl correspondence for the holomorphic representations of the Jacobi group. (English)
Keyword: Berezin quantization
Keyword: Berezin transform
Keyword: quasi-Hermitian Lie group
Keyword: unitary representation
Keyword: holomorphic representation
Keyword: reproducing kernel Hilbert space
Keyword: Jacobi group
Keyword: Stratonovich-Weyl correspondence
Keyword: coadjoint orbit
MSC: 22E10
MSC: 22E27
MSC: 32M05
MSC: 32M10
MSC: 32M15
MSC: 46E22
MSC: 81S10
idZBL: Zbl 1304.22005
idMR: MR3233725
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Date available: 2014-08-27T08:55:35Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/143904
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Reference: [1] Ali, S.T., Englis, M.: Quantization methods: a guide for physicists and analysts.Rev. Math. Phys., 17, 4, 2005, 391-490, Zbl 1075.81038, MR 2151954, 10.1142/S0129055X05002376
Reference: [2] Arazy, J., Upmeier, H.: Invariant symbolic calculi and eigenvalues of invariant operators on symmetric domains. Function spaces, interpolation theory and related topics (Lund, 2000) 151--211.2002, De Gruyter, Berlin, MR 1943284
Reference: [3] Arazy, J., Upmeier, H.: Weyl Calculus for Complex and Real Symmetric Domains, Harmonic analysis on complex homogeneous domains and Lie groups (Rome, 2001).Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 13, 3--4, 2002, 165-181, MR 1984098
Reference: [4] Berceanu, S.: A holomorphic representation of the Jacobi algebra.Rev. Math. Phys., 18, 2006, 163-199, Zbl 1099.81036, MR 2228923, 10.1142/S0129055X06002619
Reference: [5] Berceanu, S., Gheorghe, A.: On the geometry of Siegel-Jacobi domains.Int. J. Geom. Methods Mod. Phys., 8, 2011, 1783-1798, Zbl 1250.22010, MR 2876095
Reference: [6] Berezin, F.A.: Quantization.Math. USSR Izv., 8, 5, 1974, 1109-1165, Zbl 0312.53049
Reference: [7] Berezin, F.A.: Quantization in complex symmetric domains.Math. USSR Izv., 9, 2, 1975, 341-379, 10.1070/IM1975v009n02ABEH001480
Reference: [8] Berndt, R., Böcherer, S.: Jacobi forms and discrete series representations of the Jacobi group.Math. Z., 204, 1990, 13-44, Zbl 0695.10024, MR 1048065, 10.1007/BF02570858
Reference: [9] Berndt, R., Schmidt, R.: Elements of the representation theory of the Jacobi group, Progress in Mathematics 163.1998, Birkhäuser Verlag, Basel, MR 1634977
Reference: [10] Cahen, B.: Berezin quantization for discrete series.Beiträge Algebra Geom., 51, 2010, 301-311, MR 2682458
Reference: [11] Cahen, B.: Stratonovich-Weyl correspondence for compact semisimple Lie groups.Rend. Circ. Mat. Palermo, 59, 2010, 331-354, Zbl 1218.22008, MR 2745515, 10.1007/s12215-010-0026-y
Reference: [12] Cahen, B.: Stratonovich-Weyl correspondence for discrete series representations.Arch. Math. (Brno), 47, 2011, 41-58, Zbl 1240.22011, MR 2813546
Reference: [13] Cahen, B.: Berezin Quantization and Holomorphic Representations.Rend. Sem. Mat. Univ. Padova, 129, 2013, 277-297, Zbl 1272.22007, MR 3090642, 10.4171/RSMUP/129-16
Reference: [14] Cahen, B.: Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 52, 2013, 35-48, Zbl 1296.22007, MR 3202747
Reference: [15] Cariñena, J.F., Gracia-Bondìa, J.M., Vàrilly, J.C.: Relativistic quantum kinematics in the Moyal representation.J. Phys. A: Math. Gen., 23, 1990, 901-933, Zbl 0706.60108, MR 1048769, 10.1088/0305-4470/23/6/015
Reference: [16] Davidson, M., Òlafsson, G., Zhang, G.: Laplace and Segal-Bargmann transforms on Hermitian symmetric spaces and orthogonal polynomials.J. Funct. Anal., 204, 2003, 157-195, Zbl 1035.32014, MR 2004748, 10.1016/S0022-1236(03)00101-0
Reference: [17] Figueroa, H., Gracia-Bondìa, J.M., Vàrilly, J.C.: Moyal quantization with compact symmetry groups and noncommutative analysis.J. Math. Phys., 31, 1990, 2664-2671, MR 1075750, 10.1063/1.528967
Reference: [18] Folland, B.: Harmonic Analysis in Phase Space.1989, Princeton Univ. Press, Zbl 0682.43001, MR 0983366
Reference: [19] Gracia-Bondìa, J.M.: Generalized Moyal quantization on homogeneous symplectic spaces, Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990), 93--114, Contemp. Math., 134.1992, Amer. Math. Soc., Providence, RI, MR 1187280
Reference: [20] Gracia-Bondìa, J.M., V¸rilly, J.C.: The Moyal Representation for Spin.Ann. Physics, 190, 1989, 107-148, MR 0994048
Reference: [21] Kirillov, A.A.: Lectures on the Orbit Method, Graduate Studies in Mathematics, Vol. 64.2004, American Mathematical Society, Providence, Rhode Island, MR 2069175, 10.1090/gsm/064
Reference: [22] Neeb, K-H.: Holomorphy and Convexity in Lie Theory, de Gruyter Expositions in Mathematics, Vol. 28.2000, Walter de Gruyter, Berlin, New-York, MR 1740617
Reference: [23] Nomura, T.: Berezin Transforms and Group representations.J. Lie Theory, 8, 1998, 433-440, Zbl 0919.43008, MR 1650386
Reference: [24] Ørsted, B., Zhang, G.: Weyl Quantization and Tensor Products of Fock and Bergman Spaces.Indiana Univ. Math. J., 43, 2, 1994, 551-583, Zbl 0805.46053, MR 1291529, 10.1512/iumj.1994.43.43023
Reference: [25] Peetre, J., Zhang, G.: A weighted Plancherel formula III. The case of a hyperbolic matrix ball.Collect. Math., 43, 1992, 273-301, MR 1252736
Reference: [26] Satake, I.: Algebraic structures of symmetric domains.1971, Iwanami Sho-ten, Tokyo and Princeton Univ. Press, Princeton, NJ, MR 0591460
Reference: [27] Stratonovich, R.L.: On distributions in representation space.Soviet Physics. JETP, 4, 1957, 891-898, MR 0088173
Reference: [28] Unterberger, A., Upmeier, H.: Berezin transform and invariant differential operators.Commun. Math. Phys., 164, 3, 1994, 563-597, Zbl 0843.32019, MR 1291245, 10.1007/BF02101491
Reference: [29] Zhang, G.: Berezin transform on compact Hermitian symmetric spaces.Manuscripta Math., 97, 1998, 371-388, Zbl 0920.22008, MR 1654800, 10.1007/s002290050109
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