Glasnik Matematicki, Vol. 43, No.2 (2008), 337-362.
THE STRUCTURES OF STANDARD (g,K)-MODULES OF SL(3,R)
Tadashi Miyazaki
Department of Mathematical Sciences, University of Tokyo, Japan
e-mail: miyaza@ms.u-tokyo.ac.jp
Abstract. We describe explicitly the structures of standard
(,K)-modules of SL(3,R).
2000 Mathematics Subject Classification.
22E46, 11F70.
Key words and phrases. Semisimple Lie group, principal series representation,
generalized principal series representation.
Full text (PDF) (free access)
DOI: 10.3336/gm.43.2.08
References:
- D. Bump,
Automorphic forms and representations, Cambridge Studies in Advanced Mathematics 55,
Cambridge University Press, Cambridge, 1997.
MathSciNet
- T. Fujimura,
On some degenerate principal series representations of O(p,2),
J. Lie Theory 11 (2001), 23-55.
MathSciNet
- R. Howe,
K-type structure in the principal series of GL3. I,
in: Analysis on homogeneous spaces and representation theory of
Lie groups, Okayama--Kyoto (1997), volume 26 of Adv. Stud. Pure Math.,
pages 77-98. Math. Soc. Japan, Tokyo, 2000.
MathSciNet
- R. E. Howe and E.-C. Tan,
Homogeneous functions on light cones: the infinitesimal structure of
some degenerate principal series representations,
Bull. Amer. Math. Soc. (N.S.) 28 (1993), 1-74.
MathSciNet
CrossRef
- H. Kraljevic,
Representations of the universal convering group of the group SU(n,1),
Glas. Mat. Ser. III 8(28) (1973), 23-72.
MathSciNet
- S. T. Lee,
Degenerate principal series representations of Sp(2n,R),
Compositio Math. 103 (1996), 123-151.
MathSciNet
Numdam
- S. T. Lee and H. Y. Loke,
Degenerate principal series representations of Sp(p,q),
Israel J. Math. 137 (2003), 355-379.
MathSciNet
CrossRef
- H. Manabe, T. Ishii, and T. Oda,
Principal series Whittaker functions on SL(3,R),
Japan. J. Math. (N.S.) 30 (2004), 183-226.
MathSciNet
- T. Miyazaki,
Whittaker functions for generalized principal series representations
of SL(3,R), Manuscripta Math., to appear.
- T. Miyazaki,
The (,K)-module structures of principal series
representations of Sp(3,R), preprint.
- T. Oda,
The standard (,K)-modules of
Sp(2,R) I, submitted.
- E. Thieleker,
On the integrable and square-integrable representations of Spin(1,2m),
Trans. Amer. Math. Soc. 230 (1977), 1-40.
MathSciNet
CrossRef
Glasnik Matematicki Home Page