Categories of unitary representations of Banach-Lie supergroups and restriction functors

Pacific Journal of Mathematics

Volumn 257, Issue 2, 2012, Pages 431-469

  Merigon, Stéphane ^a   Neeb, Karl Hermann ^a   Salmasian, Hadi ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Analytic vectors; Banach Lie supergroups; Smooth vectors; Unitary representations

Indexed keywords

EID: 84866542229     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2012.257.431     Document Type: Article

References (36)

1. A. Alldridge and M. Laubinger, "Infinite-dimensional supermanifolds over arbitrary base fields", Forum Math. 24:3 (2012), 565-608.
2. A. Alldridge, J. Hilgert, and M. Laubinger, "Harmonic analysis on Heisenberg- Clifford Lie supergroups", preprint, 2011.
3. J. Bochnak and J. Siciak, "Polynomials and multilinear mappings in topological vector spaces", Studia Math. 39 (1971), 59-76.
4. J. Bochnak and J. Siciak, "Analytic functions in topological vector spaces", Studia Math. 39 (1971), 77-112.
5. W. Boucher, D. Friedan, and A. Kent, "Determinant formulae and unitarity for the N D 2 superconformal algebras in two dimensions or exact results on string compactification", Phys. Lett. B 172:3-4 (1986), 316-322.
6. N. Bourbaki, Variétés différentielles et analytiques: fascicule de résultats (paragraphes 1 à 7), Actualités Scientifiques et Industrielles 1333, Hermann, Paris, 1967.
7. C. Carmeli, G. Cassinelli, A. Toigo, and V. S. Varadarajan, "Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles", Comm. Math. Phys. 263:1 (2006), 217-258.
8. P. Deligne and J. W. Morgan, "Notes on supersymmetry (following Joseph Bernstein)", pp. 41-97 in Quantum fields and strings: a course for mathematicians (Princeton, NJ, 1996-1997), vol. 1, edited by P. Deligne et al., Amer. Math. Soc., Providence, RI, 1999.
9. N. Dunford and J. T. Schwartz, Linear operators, II: Spectral theory, Wiley, New York, 1988.
10. S. Ferrara, C. A. Savoy, and B. Zumino, "General massive multiplets in extended supersymmetry", Phys. Lett. B 100:5 (1981), 393-398.
11. D. Friedan, Z. Qiu, and S. Shenker, "Superconformal invariance in two dimensions and the tricritical Ising model", Phys. Lett. B 151:1 (1985), 37-43.
12. P. Goddard, A. Kent, and D. Olive, "Unitary representations of the Virasoro and super-Virasoro algebras", Comm. Math. Phys. 103:1 (1986), 105-119.
13. E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications 31, Amer. Math. Soc., Providence, RI, 1974.
14. K. Iohara, "Unitarizable highest weight modules of the N D 2 super Virasoro algebras: untwisted sectors", Lett. Math. Phys. 91:3 (2010), 289-305.
15. H. P. Jakobsen and V. G. Kac, "A new class of unitarizable highest weight representations of infinite-dimensional Lie algebras, II", J. Funct. Anal. 82:1 (1989), 69-90.
16. P. D. Jarvis and R. B. Zhang, "Unitary Sugawara constructions for affine superalgebras", Phys. Lett. B 215:4 (1988), 695-700.
17. P. E. T. Jørgensen and R. T. Moore, Operator commutation relations: commutation relations for operators, semigroups, and resolvents with applications to mathematical physics and representations of Lie groups, Reidel, Dordrecht, 1984.
18. V. G. Kac and I. T. Todorov, "Superconformal current algebras and their unitary representations", Comm. Math. Phys. 102:2 (1985), 337-347.
19. A. A. Kirillov, "Representations of the infinite-dimensional unitary group", Dokl. Akad. Nauk. SSSR 212 (1973), 288-290. In Russian; translated in Sov. Math. Dokl. 14 (1973), 1355-1358.
20. B. Kostant, "Graded manifolds, graded Lie theory, and prequantization", pp. 177-306 in Differential geometrical methods in mathematical physics (Bonn, 1975), edited by K. Bleuler and A. Reetz, Lecture Notes in Math. 570, Springer, Berlin, 1977.
21. S. Merigon, "Integrating representations of Banach-Lie algebras", J. Funct. Anal. 260:5 (2011), 1463-1475.
22. K.-H. Neeb, "Semi-bounded unitary representations of infinite-dimensional Lie groups", pp. 209-222 in Infinite dimensional harmonic analysis, IV (Tokyo, 2007), edited by J. Hilgert et al., World Scientific, Hackensack, NJ, 2009.
23. K.-H. Neeb, "On differentiable vectors for representations of infinite dimensional Lie groups", J. Funct. Anal. 259:11 (2010), 2814-2855.
24. K.-H. Neeb, "Semibounded representations and invariant cones in infinite dimensional Lie algebras", Confluentes Math. 2:1 (2010), 37-134.
25. K.-H. Neeb, "On analytic vectors for unitary representations of infinite dimensional Lie groups", Ann. Inst. Fourier 61:5 (2011), 1839-1874.
26. E. Nelson, "Analytic vectors", Ann. of Math. (2) 70:3 (1959), 572-615.
27. G. I. Ol'shanskǐi, "Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians", pp. 1-66 in Topics in representation theory, edited by A. A. Kirillov, Adv. Soviet Math. 2, Amer. Math. Soc., Providence, RI, 1991.
28. M. Reed and B. Simon, Methods of modern mathematical physics, I: Functional analysis, Academic Press, New York, 1972.
29. W. Rudin, Function theory in the unit ball of Cn, Grundlehren der Mathematischen Wissenschaften 241, Springer, New York, 1980.
30. W. Rudin, Real and complex analysis, 3rd ed., McGraw-Hill, New York, 1987.
31. A. Salam and J. Strathdee, "Unitary representations of super-gauge symmetries", Nuclear Phys. B 80:3 (1974), 499-505.
32. H. Salmasian, "Unitary representations of nilpotent super Lie groups", Comm. Math. Phys. 297:1 (2010), 189-227.
33. F. Sauvageot, "Représentations unitaires des super-algèbres de Ramond et de Neveu-Schwarz", Comm. Math. Phys. 121:4 (1989), 639-657.
34. G. Segal, "Unitary representations of some infinite dimensional groups", Comm. Math. Phys. 80:3 (1981), 301-342.
35. J. Siciak, "A polynomial lemma and analytic mappings in topological vector spaces", pp. 131-142 in Séminaire Pierre Lelong (Analyse) (Paris, 1970-1971), edited by P. Lelong, Lecture Notes in Math. 275, Springer, Berlin, 1972.
36. V. S. Varadarajan, An introduction to harmonic analysis on semisimple Lie groups, Cambridge Studies in Advanced Mathematics 16, Cambridge University Press, Cambridge, 1999.