Eigenfunction expansion associated with the Casimir operator on the quantum group $SU_q(1,1)$

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Eigenfunction expansion associated with the Casimir operator on the quantum group $SU_q(1,1)$

Tomoyuki Kakehi

Source: Duke Math. J. Volume 80, Number 2 (1995), 535-573.

First Page: Show

Primary Subjects: 33D80

Secondary Subjects: 17B37, 81R50

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077246091
Mathematical Reviews number (MathSciNet): MR1369401
Zentralblatt MATH identifier: 0846.17014
Digital Object Identifier: doi:10.1215/S0012-7094-95-08019-3

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References

[B] V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568–640.

Mathematical Reviews (MathSciNet): MR9,133a

Zentralblatt MATH: 0045.38801

Digital Object Identifier: doi:10.2307/1969129

JSTOR: links.jstor.org

[J] M. Jimbo, A $q$-difference analogue of $U(\germ g)$ and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), no. 1, 63–69.

Mathematical Reviews (MathSciNet): MR86k:17008

Zentralblatt MATH: 0587.17004

Digital Object Identifier: doi:10.1007/BF00704588

[KMU1] T. Kakehi, T. Masuda, and K. Ueno, Spectrum of an operator appears in the quantum $\rm SU(1,1)$ group, Quantum and non-commutative analysis (Kyoto, 1992), Math. Phys. Stud., vol. 16, Kluwer Acad. Publ., Dordrecht, 1993, pp. 253–261.

Mathematical Reviews (MathSciNet): MR95b:81092

Zentralblatt MATH: 0847.47018

[KMU2] T. Kakehi, T. Masuda, and K. Ueno, Spectral analysis of a $q$-difference operator which arises from the quantum $SU(1,1)$ group, to appear in J. Operator Theory.

Mathematical Reviews (MathSciNet): MR1342480

Zentralblatt MATH: 0839.47014

[Ko1] L. Korogodsky, Quantum group $\rm SU(1,1)\rtimes Z\sb 2$ and “super-tensor” products, Comm. Math. Phys. 163 (1994), no. 3, 433–460.

Mathematical Reviews (MathSciNet): MR95g:81081

Zentralblatt MATH: 0833.17020

Digital Object Identifier: doi:10.1007/BF02101457

Project Euclid: euclid.cmp/1104270579

[Ko2] L. Korogodsky, Quantum projective spaces, spheres and hyperboloids, preprint.

[KV1] L. Korogodsky and L. Vaksman, Harmonic analysis on quantum hyperboloids, preprint ITP-90-27P, Institute of Theoretical Physics, Kiev, 1990.

[KV2] L. Korogodsky and L. Vaksman, Spherical functions on the quantum group $SU_q(1, 1)$ and a $q$-analogue of Fok-Mehler's formula, Funktsional Anal. i Prilozhen 25 (1991), 60–62.

Zentralblatt MATH: 0726.43012

[MMNNU] T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi, and K. Ueno, Representations of the quantum group $\rm SU\sb q(2)$ and the little $q$-Jacobi polynomials, J. Funct. Anal. 99 (1991), no. 2, 357–386.

Mathematical Reviews (MathSciNet): MR93c:17027

Zentralblatt MATH: 0737.33012

Digital Object Identifier: doi:10.1016/0022-1236(91)90045-7

[MMNNSU]¹ T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi, Y. Saburi, and K. Ueno, Unitary representations of the quantum group $\rm SU\sb q(1,1)$. Structure of the dual space of $U\sb q(\germ s\germ l(2))$, Lett. Math. Phys. 19 (1990), no. 3, 187–194.

Mathematical Reviews (MathSciNet): MR91h:33028

Zentralblatt MATH: 0704.17007

Digital Object Identifier: doi:10.1007/BF01039311

[MMNNSU]² T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi, Y. Saburi, and K. Ueno, Unitary representations of the quantum group $\rm SU\sb q(1,1)$. II. Matrix elements of unitary representations and the basic hypergeometric functions, Lett. Math. Phys. 19 (1990), no. 3, 195–204.

Mathematical Reviews (MathSciNet): MR91h:33029

Zentralblatt MATH: 0704.17008

Digital Object Identifier: doi:10.1007/BF01039312

[MW] T. Masuda and J. Watanabe, Sur les espaces vectoriels topologiques associés aux groupes quantiques $\rm SU\sb q(2)$ et $\rm SU\sb q(1,1)$, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 11, 827–830.

Mathematical Reviews (MathSciNet): MR92b:58022

Zentralblatt MATH: 0752.17015

[Mi] K. Mimachi, Connection problem in holonomic $q$-difference system associated with a Jackson integral of Jordan-Pochhammer type, Nagoya Math. J. 116 (1989), 149–161.

Mathematical Reviews (MathSciNet): MR91b:33023

Zentralblatt MATH: 0688.39002

Project Euclid: euclid.nmj/1118781433

[PW] P. Podles and S. Woronowicz, Quantum deformation of Lorentz group, Comm. Math. Phys. 130 (1990), no. 2, 381–431.

Mathematical Reviews (MathSciNet): MR91f:46100

Zentralblatt MATH: 0703.22018

Digital Object Identifier: doi:10.1007/BF02473358

Project Euclid: euclid.cmp/1104200517

[Sl] L. Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966.

Mathematical Reviews (MathSciNet): MR34:1570

Zentralblatt MATH: 0135.28101

[SV] Y. Soibelman and L. Vaksman, On some problems in the theory of quantum groups, Representation theory and dynamical systems, Adv. Soviet Math., vol. 9, Amer. Math. Soc., Providence, RI, 1992, pp. 3–55.

Mathematical Reviews (MathSciNet): MR93h:17043

Zentralblatt MATH: 0766.58007

[Su] M. Sugiura, Unitary representations and harmonic analysis, Kodansha Ltd., Tokyo, 1975.

Mathematical Reviews (MathSciNet): MR58:16977

Zentralblatt MATH: 0344.22001

[U] K. Ueno, Spectral analysis for the Casimir operator on the quantum group $\rm SU\sb q(1,1)$, Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 2, 42–44.

Mathematical Reviews (MathSciNet): MR91g:33025

Zentralblatt MATH: 0721.17015

Digital Object Identifier: doi:10.3792/pjaa.66.42

Project Euclid: euclid.pja/1195512593

[W1] S. Woronowicz, Twisted $\rm SU(2)$ group. An example of a noncommutative differential calculus, Publ. Res. Inst. Math. Sci. 23 (1987), no. 1, 117–181.

Mathematical Reviews (MathSciNet): MR88h:46130

Zentralblatt MATH: 0676.46050

Digital Object Identifier: doi:10.2977/prims/1195176848

[W2] S. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613–665.

Mathematical Reviews (MathSciNet): MR88m:46079

Zentralblatt MATH: 0627.58034

Digital Object Identifier: doi:10.1007/BF01219077

Project Euclid: euclid.cmp/1104159726

[Y] K. Yosida, Functional analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin, 1980.

Mathematical Reviews (MathSciNet): MR82i:46002

Zentralblatt MATH: 0435.46002

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