This note is based on five lectures on the geometry of flag manifolds and the representation theory of real semisimple Lie groups, delivered at the CIME summer school “Representation theory and Complex Analysis”, June 10-17, 2004, Venezia.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Beilinson and J. Bernstein, Localization de g-modules, C. R. Acad. Sci. Paris, 292(1981),15-18.
—,—, A generalization of Casselman’s submodule theorem, Represen- tation theory of reductive groups (Park City, Utah, 1982), Progr. Math., 40, Birkhäuser Boston, Boston, MA, (1983) 35-52.
A. Beilinson, J. Bernstein and P. Deligne, Faisceaux Pervers, Astérisque, 100 (1982).
J. Bernstein and V. Lunts, Equivariant sheaves and functors, Lecture Notes in Mathematics, 1578, Springer-Verlag, Berlin, (1994).
W. Casselman, Jacquet modules for real reductive groups, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, (1980) 557-563.
A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), Advanced Studies in Pure Mathematics, 2, North-Holland Publishing Co. (1968).
Harish-Chandra, Representation of a semisimple Lie group on a Banach space I, Trans. Amer. Math., Soc., 75 (1953), 185-243.
—, The characters of semisimple Lie groups, ibid., 83 (1956), 98-163.
—, Invariant eigendistributions on semisimple Lie groups, ibid., 119 (1965), 457-508.
—, Discrete series for semisimple Lie groups I, Acta Math. 113 (1965), 241-318.
H. Hecht and J. L. Taylor, Analytic localization of group representations. Adv. Math. 79 no. 2 (1990), 139-212.
M. Kashiwara, The Riemann-Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci. 20 (1984), no. 2, 319-365.
—, Character, character cycle, fixed point theorem and group representations, Advanced Studies in Pure Math., 14 (1988) 369-378.
—, Open problems in group representation theory, Proceeding of Taniguchi Symposium held in 1986, RIMS preprint 569.
—, Representation theory and D -modules on flag manifolds, Astérisque 173-174(1989) 55-109.
—, D-modules and microlocal calculus, Translated from the 2000 Japanese original by Mutsumi Saito, Translations of Mathematical Monographs 217 Iwanami Series in Modern Mathematics, American Mathematical Society, Providence, RI (2003).
M. Kashiwara, A. Kowata, K. Minemura, K. Okamoto, T. Oshima, M. Tanaka, Eigenfunctions of invariant differential operators on a symmetric space, Ann. of Math. (2) 107 (1978), no. 1, 1-39.
M. Kashiwara and P. Schapira, Sheaves on Manifold, Grundlehren der Mathe-matischen Wissenschaften 292, Springer (1990).
—, Categories and sheaves, Grundlehren der Mathematischen Wissenschaften 332, Springer-Verlag, Berlin, (2006).
—, Moderate and formal cohomology associated with constructible sheaves, Mém. Soc. Math. France (N.S.) 64, (1996).
M. Kashiwara and W. Schmid, Quasi-equivariant D-modules, equivariant derived category, and representations of reductive Lie groups, Lie theory and geometry, Progr. Math., 123, Birkhäuser, (1994) 457-488.
T. Matsuki, Orbits on affine symmetric spaces under the action of parabolic subgroups, Hiroshima Math., J., 12 (1982), 307-320.
I. Mirković, T. Uzawa and K. Vilonen, Matsuki correspondence for sheaves, Invent. Math., 109 (1992), 231-245.
S. J. Prichepionok, A natural topology for linear representations of semisimple Lie algebras, Soviet Math. Doklady 17 (1976) 1564-1566.
W. Schmid, Boundary value problems for group invariant differential equations, Élie Cartan et les Mathématiques d’aujourd’hui, Astérisque, (1985), 311-322.
J.-P. Schneiders, Quasi-abelian categories and sheaves, Mém. Soc. Math. Fr. (N.S.) 76 (1999).
L. Smithies and J. L. Taylor, An analytic Riemann-Hilbert correspondence for semi-simple Lie groups, Represent. Theory 4 (2000), 398-445 (electronic)
H. Sumihiro, Equivariant completion, J. Math. Kyoto Univ. 14 (1974), 1-28.
W. Schmid and J. A. Wolf, Globalizations of Harish-Chandra modules, Bulletin of AMS, 17 (1987), 117-120.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kashiwara, M. (2008). Equivariant Derived Category and Representation of Real Semisimple Lie Groups. In: Tarabusi, E.C., D'Agnolo, A., Picardello, M. (eds) Representation Theory and Complex Analysis. Lecture Notes in Mathematics, vol 1931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76892-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-76892-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76891-3
Online ISBN: 978-3-540-76892-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)