Abstract
In this paper we discuss some of the basic general notions and results which play a key role in the representation theory of infinite-dimensional Lie groups modeled over sequentially complete locally convex (s.c.l.c.) spaces. In the following each locally convex space will implicitly be assumed to be Hausdorff.
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References
Bourbaki, N., “Integration,” Chap. 6, Hermann, Paris, 1959
Bourbaki, N., “Topologie Generale,” Chap. 10, Hermann, Paris, 1971
Bourbaki, N., “Topological Vector Spaces,” Chap. 1–5, Springer-Verlag, 1987
Frohlicher, A., and A. Kriegl, “Linear Spaces and Differentiation Theory,” J. Wiley, Interscience, 1988
[G199] Glockner, H., Direct limit Lie groups and manifolds, Kyoto J. Math., to appear
Grabowski, J., Derivative of the exponential mapping for infinite-dimensional Lie groups, Preprint, 1997
Hamilton, R., The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. 7 (1982), 65–222
Herve, M., “Analytic and Plurisubharmonic Functions,” Lecture Notes in Mathematics 198, Springer Verlag, Berlin, 1971
Herve, M., “Analyticity in Infinite-dimensional Spaces,” de Gruyter, Berlin, 1989
Hille, E., and R.S. Phillips, “Functional Analysis and Semigroups,” Amer. Math. Soc. Colloquium Publications XXXI, Providence, Rhode Island, 1957
Husemoller, D., “Fibre Bundles,” Graduate Texts in Math., Springer, New York, 1994
Kac, V. G., “Infinite-dimensional Groups with Applications,” Mathematical Sciences Research Institute Publications 4, Springer-Verlag, Berlin, Heidelberg, New York, 1985
Keller, H. H., “Differential Calculus in Locally Convex Spaces,” Lecture Notes in Math. 417, Springer Verlag, 1974
Kirillov, A. A., “Elements of the Theory of Representations,” Grundlehren der mathematischen Wissenschaften 220, Springer-Verlag, Berlin, Heidelberg, 1976
Kriegl, A., and P. W. Michor, “The Convenient Setting of Global Analysis,” Amer. Math. Soc., Providence R. I., 1997
Kriegl, A., and P. W. Michor, Regular infinite-dimensional Lie groups, Journal of Lie Theory 7 (1997), 61–99
Lisiecki, W., Coherent state representations. A survey, Reports on Math. Phys. 35 (1995), 327–358
Mickelsson, J., “Current algebras and groups,” Plenum Press, New York, 1989
Milnor, J., Remarks on infinite-dimensional Lie groups, Proc Summer School on Quantum Gravity, Ed. B. DeWitt, Les Houches, 1983
Nachbin, L., “Topology on Spaces of Holomorphic Mappings,” Ergebnisse der Math. 47, Springer Verlag, Berlin, 1969
Natarajan, L., Rodriquez-Carrington, E., and J. A. Wolf, Differentiable struc- ture for direct limit groups, Letters in Mathematical Physics 23 (1991), 99–109
Natarajan, L., Locally convex Lie groups, Nova Journal of Algebra and Geometry 2:1 (1993), 59–87
Natarajan, L., New classes of infinite-dimensional Lie groups, Proceedings of Symposia in Pure Math. 56:2 (1994), 59–87
Neeb, K.-H., Borel-Weil theory for loop groups, in this volume
Pressley, A., and G. Segal, “Loop Groups,” Oxford University Press, Oxford, 1986
Thomas, E. G. F., Vector fields as derivations on nuclear manifolds, Math. Nachr. 176 (1995), 277–286
Thomas, E. G. F., Calculus on locally convex spaces, Preprint W-9604, Univ. of Groningen, 1996
Treves, F., “Topological Vector Spaces, distributions, and kernels,” Academic Press, New York, 1967
Warner, G., “Harmonic Analysis on Semisimple Lie Groups I,” Springer, Berlin, Heidelberg, New York, 1972
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Neeb, KH. (2001). Infinite-dimensional Groups and their Representations. In: Huckleberry, A., Wurzbacher, T. (eds) Infinite Dimensional Kähler Manifolds. DMV Seminar Band, vol 31. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8227-9_2
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DOI: https://doi.org/10.1007/978-3-0348-8227-9_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6602-5
Online ISBN: 978-3-0348-8227-9
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