Special prehomogeneous vector spaces associated to F4, E6, E7, E8 and simple Jordan algebras of rank 3

Journal of Algebra

Volumn 264, Issue 1, 2003, Pages 98-128

  Clerc, Jean Louis ^a  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

Conformal group; Exceptional simple Lie algebra; Prehomogeneous vector space; Simple Jordan algebra; Symmetric space of quanternionic type

Indexed keywords

EID: 0037671896     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(03)00115-7     Document Type: Article

References (26)

1. W. Bertram, Un théorème de Liouville pour les algèbres de Jordan, Bull. Soc. Math. France 124 (1996) 299-327.
2. H. Braun, M. Koecher, Jordan-Algebren, Springer-Verlag, Berlin, 1966.
3. N. Bourbaki, Groupes et algèbres de Lie, Eléments de mathématique, Masson, Paris, 1981.
4. J.-L. Clerc, B. Øersted, The Maslov index revisited, Transformation Groups 6 (2001) 303-320.
5. R. Donagi, On the Geometry of Grassmannians, Duke Math. J. 44 (1977) 795-837.
6. J. Faraut, S. Gindikin, Pseudo-Hermitian symmetric spaces of tube type, in: Progress in Nonlinear Diff. Equat., Vol. 20, 1996, pp. 123-154.
7. J. Faraut, A. Korányi, Analysis on Symmetric Cones, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1994.
8. 8 zur Oktavienebene, Proc. Kon. Akad. Wet. I. 57 (1954) 218-230, II. 57 (1954) 363-368, III. 58 (1955) 151-157, IV. 58 (1955) 277-285.
9. B. Gross, N. Wallach, A distinguished family of unitary representations for the exceptional groups of real rank 4, in: Lie Theory and Geometry, Birkhäuser, 1994, pp. 289-304.
10. B. Gross, N. Wallach, On quaternionic discrete series representations and their continuations, J. Reine Angew. Math. 481 (1996) 73-123.
11. S. Haris, Some irreducible representations of exceptional algebraic groups, Amer. J. Math. 93 (1971) 75-106.
12. J. Igusa, A classification of spinors up to dimension 12, Amer. J. Math. 92 (1970) 997-1028.
13. A. Joseph, The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. Scient. Ec. Norm. Sup. 9 (1976) 1-30.
14. J.M. Landsberg, L. Manivel, The projective geometry of Freudenthal's magic square, J. Algebra 239 (2001) 477-512.
15. I. Muller, Racines orthogonales et orbites d'algèbres de Lie semi-simples graduées, J. Algebra 193 (1997) 41-74.
16. A.L. Onishchik, E.B. Vinberg, Lie Groups and Lie Algebras III, in: Encyclopaedia of Mathematical Sciences, Vol. 41, Springer-Verlag, Berlin, 1990.
17. G. Rohrle, On extraspecial parabolic subgroups, Contemp. Math. 153 (1993) 143-155.
18. H. Rubenthaler, Espaces préhomogenes de type parabolique, in: Lecture Math. Kyoto Univ., Vol. 14, 1988, pp. 189-221.
19. H. Rubenthaler, Les paires duales dans les algèbres de Lie reductives, Astérisque 219 (1994).
20. M. Sato, T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J. 65 (1977) 1-155.
21. I. Satake, Algebraic structures of symmetric domains, in: Kanô Memorial Lectures, Vol. 4, Iwanami Shoten and Princeton University Press, Princeton, 1980.
22. C. Segre, Sui complessi lineari di piano nello spazio a cinque dimensioni, Ann. Math. Pura ed Appl. 27 (1918) 75.
23. T.A. Springer, Jordan Algebras and Algebraic Groups, in: Erg. Math., Vol. 75, Springer-Verlag, New York, 1973.
24. J. Tits, Algèbres alternatives, algèbres de Jordan et algèbres de Lie exceptionnelles. I. Construction, Nederl. Akad. Wetensch. Proc. Ser. A 69 (1966) 223-237, Indag. Math. 28.
25. E.B. Vinberg, Classification of homogeneous nilpotent elements of a semi-simple graded Lie algebra, Selecta Math. Soviet. 6 (1987) 15-35.
26. J. Wolf, Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. Math. Mech. 14 (1965) 1033-1047.