no. 1
On the representations of U(m,n) unitarily induced from derived functor modules
Compositio Mathematica, Tome 100 (1996) no. 1, pp. 1-39 
@article{CM_1996__100_1_1_0,
     author = {Matumoto, Hisayosi},
     title = {On the representations of $U(m, n)$ unitarily induced from derived functor modules},
     journal = {Compositio Mathematica},
     pages = {1--39},
     year = {1996},
     publisher = {Kluwer Academic Publishers},
     volume = {100},
     number = {1},
     mrnumber = {1377407},
     zbl = {0858.22013},
     language = {en},
     url = {https://www.numdam.org/item/CM_1996__100_1_1_0/}
}
TY  - JOUR
AU  - Matumoto, Hisayosi
TI  - On the representations of $U(m, n)$ unitarily induced from derived functor modules
JO  - Compositio Mathematica
PY  - 1996
SP  - 1
EP  - 39
VL  - 100
IS  - 1
PB  - Kluwer Academic Publishers
UR  - https://www.numdam.org/item/CM_1996__100_1_1_0/
LA  - en
ID  - CM_1996__100_1_1_0
ER  - 
%0 Journal Article
%A Matumoto, Hisayosi
%T On the representations of $U(m, n)$ unitarily induced from derived functor modules
%J Compositio Mathematica
%D 1996
%P 1-39
%V 100
%N 1
%I Kluwer Academic Publishers
%U https://www.numdam.org/item/CM_1996__100_1_1_0/
%G en
%F CM_1996__100_1_1_0
Matumoto, Hisayosi. On the representations of $U(m, n)$ unitarily induced from derived functor modules. Compositio Mathematica, Tome 100 (1996) no. 1, pp. 1-39. https://www.numdam.org/item/CM_1996__100_1_1_0/

1 Barbasch, D.: Unipotent representations and unitarity, in: Non-Commutative Harmonic Analysis and Lie Groups, Springer Lecture Notes in Mathematics vol. 1243, Springer-Verlag, Berlin, Heidelberg, New York, 1987, 73-85. | Zbl | MR

2 Barbasch, D. and Vogan Jr., D.A.: Weyl group representations and nilpotent orbits, in: P. C. Trombi, editor, 'Representation Theory of Reductive Groups', Progress in Mathematics Vol. 40, 21-33, Birkhäuser, Boston-Basel- Stuttgart, 1983. | Zbl | MR

3 Barbasch, D. and Vogan Jr., D.A.: Unipotent representations of complex semisimple Lie groups, Ann. of Math. 121 (1985), 41-110. | Zbl | MR

4 Bien, F.: 'D-modules and Spherical Representations', Math. Notes vol. 39, Princeton University Press, Princeton, NJ, 1990. | Zbl | MR

5 Borho, W. and Brylinski, J.- L.: Differential operators on homogeneous spaces III, Invent. Math. 80 (1985), 1-68. | Zbl | MR | EuDML

6 Borho, W. and Jantzen, J.C.: Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra, Invent. Math. 39 (1977), 1-53. | Zbl | MR | EuDML

7 Chang, J.T.: Special K-types, tempered characters and the Beilinson-Bemstein realization, Duke Math. J. 56 (1988), 345-383. | Zbl | MR

8 Dixmier, J.: 'Enveloping Algebras' North-Holland, Amsterdam, New York, Oxford, 1977. | Zbl | MR

9 Enright, T.J.: Relative Lie algebra cohomology and unitary representations of complex Lie groups, Duke Math. J. 46 (1979), 513-525. | Zbl | MR

10 Gross, K.I.: The dual of parabolic subgroup and a degenerate principal series of Sp(n, C), Amer. J. Math. 93 (1971) 398-428. | Zbl | MR

11 Hecht, H., Miličič, D., Schmid, W., and Wolf, J.: Localization and standard modules for real semisimple Lie groups I: The duality theorem, Invent. Math. 90 (1987), 297-332. | Zbl | MR

12 Howe, R. and Tan, E.: Homogeneous functions on light cones: The infinitesimal structure of some degenerate principal series representations, Bull. Amer. Math. Soc. 28 (1993), 1-74. | Zbl | MR

13 Jantzen, J.C.: 'Einhüllende Algebren halbeinfacher Lie-Algebren' Ergebnisse der Mathematik und ihrer Grenzgebiete 3, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. | Zbl | MR

14 Johnson, K.D.: Degenerate principal series and compact groups, Maths. Ann. 287 (1990), 703-718. | Zbl | MR

15 Kashiwara, M. and Vergne, M.: Functions on the Shilov boundary of the generalized half-plane, in: Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics No. 728, Springer-Verlag, Berlin-Heidelberg -New York, 1979. | Zbl | MR

16 Knapp, A.W.: 'Representation Theory of Semisimple Groups, An Overview Based on Examples' Princeton Mathematical series, 36, Princeton University Press, Lawrenceville, New Jersey, 1986. | Zbl | MR

17 Knapp, A.W.: 'Lie Groups, Lie Algebras, and Cohomology' Mathematical Notes 34, Princeton University Press, Princeton, New Jersey, 1988. | Zbl | MR

18 Knapp, A.W. and Zuckerman, G.J.: Classification of irreducible tempered representations of semisimple Lie groups, Ann. of Math. 116 (1982), 389-455. | Zbl | MR

19 Kobayashi, T.: Singular unitary representations and discrete series for indefinite Stiefel manifolds U(p, q; F)/U(p - m, q; F), Memoirs of AMS vol. 462, 1992. | Zbl

20 Matsuki, T.: A description of discrete series for semisimple symmetric spaces II, Adv. Stud. in Pure Math. vol. 14, Kinokuniya Book Store and North-Holland, 1988, 531-540. | Zbl | MR

21 Matumoto, H.: Cohomological Hardy space for SU(2, 2), Adv. Stud. in Pure Math. vol. 14, Kinokuniya Book Store and North-Holland, 1988, 469-497. | Zbl | MR

22 Miličič, D.: Intertwining functors and irreducibility of standard Harish-Chandra sheaves, in: Harmonic Analysis on Reductive Groups, Progress in Mathematics vol. 101, Birkhäuser, Boston, Basel, Berlin, 1991, 209-222. | Zbl | MR

23 Mirkovic, I.: Classification of irreducible tempered representations of semisimple Lie groups, Ph.D. Thesis, Univ. of Utah, Salt Lake City, 1986.

24 Salamanca Riba, S.: On the unitary dual of some classical Lie groups, Composito Math. 68 (1988), 251-303. | Zbl | MR | Numdam

25 Sahi, S.: The Capelli identity and unitary representations, Compositio Math. 81 (1992), 247-260. | Zbl | MR | Numdam

26 Sahi, S.: Unitary representations on the Shilov boundary of a symetric tube domain, in: Representation Theory of Groups and Algebras, Contemporary Mathematics, vol. 145, American Mathematical Society, 1993, 275-286. | Zbl | MR

27 Schmid, W.: On the characters of the discrete series (the Hermitian symmetric case), Invent. Math. 30 (1975), 47-144. | Zbl | MR

28 Schmid, W.: Two character identities for semisimple Lie groups, in: Non-Commutative Harmonic Analysis, Springer Lecture Notes in Mathematics vol. 587, 1977, 196-225. | Zbl | MR

29 Schmid, W.: Geometric constructions of representations, Adv. Stud. in Pure Math. vol. 14, Kinokuniya Book Store, 349-368,1988. | Zbl | MR

30 Schmid, W.: Construction and classification of irreducible Harish-Chandra modules, in: Harmonic Analysis on Reductive Groups, Progress in Mathematics vol. 101, Birkhäuser, Boston, Basel, Berlin, 1991, 235-275. | Zbl | MR

31 Schmid, W. and Wolf, J.A.: Geometric quantization and derived functor modules for semisimple Lie group, J. of Funct. Anal. 90 (1990), 48-112. | Zbl | MR

32 Soergel, W.: Universelle versus relative Einhüllende: Eine geometrische Untersuchung von Quotientienten von universellen Einhüllenden halbeinfacher Lie-Algebren, Dissertation, Universität Hamburg, Hamburg, 1987. | Zbl

33 Speh, B.: Degenerate series representations of the universal covering group of SU(2, 2), J. Funct. Anal. 33 (1979), 95-118. | Zbl | MR

34 Speh, B. and Vogan Jr., D.A.: Reductibility of generalized series representations, Acta Math. 145 (1980), 227-299. | Zbl | MR

35 Voganjr.,D.A.: Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math. 48 (1978), 75-98. | Zbl | MR

36 Vogan Jr., D.A.: 'Representations of Real reductive Lie Groups', Progress in Mathematics, Birkhäuser, 1982. | Zbl

37 Vogan Jr., D.A.: Irreducible characters of semisimple Lie groups III, Invent. Math. 71 (1983), 381-417. | Zbl | MR

38 Vogan Jr., D.A.: Unitarizability of certain series of representations, Ann. of Math. 120 (1984), 141-187. | Zbl | MR

39 Vogan Jr., D.A.: 'Unitary Representations of reductive Lie Groups', Annuals of Mathematics Studies, Princeton University Press, 1987. | Zbl | MR

40 Vogan Jr., D.A.: The unitary dual of GL(n) over an archimedean field, Invent. Math. 83 (1986), 449-505. | Zbl | MR

41 Vogan Jr., D.A.: Irreducibilities of discrete series representations for semisimple symmetric spaces, Adv. Stud. in Pure Math. vol. 14, Kinokuniya Book Store, 1988, 381-417. | Zbl

42 Vogan Jr., D.A.: Dixmier algebras, sheets, and representation theory, in: Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Actes du colloque en l'honneur de Jacques Dixmier, Progress in Mathmatics, vol 92, Birkhäuser, Basel, Boston, 1990, 333-395. | Zbl | MR

43 Vogan Jr., D.A. and Zuckerman, G.: Unitary representations with non-zero cohomology, Compositio Math. 53 (1984), 51-90. | Zbl | MR | Numdam

44 Wallach, N.R.: On the unitarizability of derived functor modules, Invent. Math. 78 (1984), 131-141. | Zbl | MR

45 Wallach, N.R.: 'Real reductive Groups I', Academic press, 1987. | Zbl | MR