Holomorphic highest weight representations of infinite dimensional complex classical groups

Journal fur die Reine und Angewandte Mathematik

Volumn 497, Issue , 1998, Pages 171-222

  Neeb, Karl Hermann ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032428541     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.1998.038     Document Type: Article

References (36)

1. H. Araki and Wyss, Representations of Canonical Anticommutation Relations, Helv. Math. Phys. Acta 37 (1964), 137.
2. N. Bourbaki, Groupes et algèbres de Lie, Chapitres 7 et 8, Masson, Paris 1990.
3. 2, Duke Math. J. 47 (1980), 325-344.
4. A. Carey and J. Palmer, Infinite complex spin groups, J. Funct. Anal. 83:1 (1989), 1-43.
5. P.R. Halmos, A Hilbert space problem book, Springer Verlag, New York 1967.
6. P. de la Harpe, Classical Banach Lie Algebras and Banach-Lie Groups of Operators in Hubert Space, Lect. Notes Math. 285, Springer Verlag, Berlin 1972.
7. M. Hervé, Analyticity in infinite dimensional spaces, de Gruyter, Berlin 1989.
8. K.H. Hofmann, Zur mathematischen Theorie des Messens, Rozprawy Matematyczne (later Dissertationes Mathematicae) XXXII (1963).
9. D. Husemoller, Fibre Bundles, Grad. Texts Math., Springer, New York 1994.
10. V.G. Kac, Infinite dimensional Lie algebras, Cambridge University Press, 1985.
11. V.G. Kac and A.K. Raina, Highest weight representations of infinite dimensional Lie algebras, Adv. Ser. Math. Phys., World Scientific, Singapore 1987.
12. A.A. Kirillov, Representation of the infinite dimensional unitary group, Dokl. Akad. Nauk. SSSR 212 (1973), 288-290.
13. V.I. Kolomytsev and Y.S. Samoilenko, Irreducible representations of inductive limits of groups, Ukrain. Mat. Zh. 29:4 (1977), 526-531.
14. L. Natarajan, Unitary Highest Weight-Modules of Inductive Limit Lie Algebras and Groups, J. Algebra 167 (1994), 9-28.
15. L. Natarajan, E. Rodriguez-Carrington and J.A. Wolf, Differentiate Structure for Direct Limit Groups, Lett. Math. Phys. 23 (1991), 99-109.
16. L. Natarajan, E. Rodriguez-Carrington and J.A. Wolf, Locally convex Lie groups, Nova J. Alg. Geom. 2:1 (1993), 59-87.
17. L. Natarajan, E. Rodriguez-Carrington and J.A. Wolf, New Classes of Infinite Dimensional Lie Groups, Proc. Symp. Pure Math. 56:2 (1994), 377-392.
18. L. Natarajan, E. Rodriguez-Carrington and J.A. Wolf, The Bott-Borel Weil Theorem for Direct Limit Groups, Preprint 1997.
19. K.-H. Neeb, Holomorphic representation theory II, Acta math. 173:1 (1994), 103-133.
20. K.-H. Neeb, On a Theorem of S. Banach, J. Lie Th. 7:2 (1997), 293-300.
21. K.-H. Neeb, Holomorphy and Convexity in Lie Theory, Expos. Math., de Gruyter, in preparation.
22. K.-H. Neeb and B. Ørsted, Unitary Highest Weight Representations in Hilbert Spaces of Holomorphic Functions on Infinite Dimensional Domains, J. Funct. Anal., to appear.
23. Y.A. Neretin, Categories of Symmetries and Infinite-Dimensional Groups, London Math. Soc. Monogr., New Series 16, Clarendon Press, Oxford 1996.
24. 0(p, ∞), Sp(p, ∞) and the corresponding motion groups, Funct. Anal. Appl. 12 (1978), 185-191.
25. J.T. Ottesen, Infinite Dimensional Groups and Algebras in Quantum Physics, Lect. Notes Phys. m27, Springer Verlag, 1995.
26. R.S. Palais, On the homotopy type of certain groups of operators, Topology 3 (1965), 271-279.
27. T.D. Palev, Highest weight irreducible unitary representations of Lie algebras of infinite matrices. I. The algebra gl(∞), J. Math. Phys. 31:3 (1990), 579-586.
28. ∞, Funkts. Anal. Prilozhen 24:1 (1990), 82-83.
29. D. Pickrell, The separable representations of U(ℋ), Proc. Amer. Math. Soc. 102 (1988), 416-420.
30. D. Pickrell, Separable representations for Automorphism groups of Infinite Symmetric Spaces, J. Funct. Anal. 90 (1990), 1-26.
31. A. Pressley and G. Segal, Loop groups, Oxford University Press, Oxford 1986.
32. S. Reed and B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators, Academic Press, New York 1978.
33. I.E. Segal, The structure of a class of representations of the unitary group on a Hubert space, Proc. Amer. Math. Soc. 81 (1957), 197-203.
34. S. Stratila and D. Voiculescu, Representations of AF algebras and of the group U(∞), Lect. Notes Math. 486, Springer Verlag, 1975.
35. A.M. Versik and S.V. Kerov, Character and factor representations of the infinite unitary group, Soviet Math. Dokl. 23:2 (1981), 389-392.
36. 1 de U(∞), J. Math, pures appl. 55 (1976), 1-20.