Local geometry of orbits for an ordinary classical lie supergroup

Tomasz Przebinda

Open Mathematics (2006)

  • Volume: 4, Issue: 3, page 449-506
  • ISSN: 2391-5455

Abstract

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In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.

How to cite

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Tomasz Przebinda. "Local geometry of orbits for an ordinary classical lie supergroup." Open Mathematics 4.3 (2006): 449-506. <http://eudml.org/doc/269329>.

@article{TomaszPrzebinda2006,
abstract = {In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.},
author = {Tomasz Przebinda},
journal = {Open Mathematics},
keywords = {17B05; 17B75; 22E15},
language = {eng},
number = {3},
pages = {449-506},
title = {Local geometry of orbits for an ordinary classical lie supergroup},
url = {http://eudml.org/doc/269329},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Tomasz Przebinda
TI - Local geometry of orbits for an ordinary classical lie supergroup
JO - Open Mathematics
PY - 2006
VL - 4
IS - 3
SP - 449
EP - 506
AB - In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.
LA - eng
KW - 17B05; 17B75; 22E15
UR - http://eudml.org/doc/269329
ER -

References

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  1. [1] N. Burgoyne and R. Cushman: “Conjugacy Classes in Linear Groups”, J. Algebra, Vol. 44, (1975), pp. 339–362. http://dx.doi.org/10.1016/0021-8693(77)90186-7 
  2. [2] D. Collingwood and W. McGovern: Nilpotent orbits in complex semisimple Lie algebras, Reinhold, Van Nostrand, New York, 1993. Zbl0972.17008
  3. [3] A. Daszkiewicz, W. Kraśkiewicz and T. Przebinda: “Dual Pairs and Kostant-Sekiguchi Correspondence. II. Classification of Nilpotent Elements”, Centr. Eur. J. Math., Vol. 3, (2005), pp. 430–464. Zbl1107.22007
  4. [4] Harish-Chandra: “Invariant Distributions on Lie algebras”, Amer. J. of Math., Vol. 86, (1964), pp. 271–309. Zbl0131.33302
  5. [5] R. Howe: Analytic Preliminaries, preprint. 
  6. [6] R. Howe: “Remarks on classical invariant theory”, Trans. Amer. Math. Soc., Vol. 313, (1989), pp. 539–570 http://dx.doi.org/10.2307/2001418 Zbl0674.15021
  7. [7] R. Howe: “Transcending Classical Invariant Theory”, J. Amer. Math. Soc., Vol. 2, (1989), pp. 535–552. http://dx.doi.org/10.2307/1990942 Zbl0716.22006
  8. [8] V. Kac: “Lie superalgebras”, Adv. Math., Vol. 26, (1977), pp. 8–96. http://dx.doi.org/10.1016/0001-8708(77)90017-2 
  9. [9] B. Kostant: Graded manifolds, graded Lie theory, and prequantization, Lecture Notes in Math., Vol. 570, Springer-Verlag, Berlin-New York, 1977, pp. 177–306. 
  10. [10] M. Spivak: A comprehensive introduction to differential geometry, Brandeis University, Waltham, Massachusetts, 1970. 
  11. [11] V.S. Varadarajan: Harmonic Analysis on Real Reductive Groups I and II, Lecture Notes in Math., Vol. 576, Springer Verlag, 1977. Zbl0354.43001
  12. [12] N. Wallach: Real Reductive Groups I, Academic Press, INC, 1988. 

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