The Maslov triple index on the Shilov boundary of a classical domain

Let D be an irreducible Hermitian symmetric space of tube-type, S its Shilov boundary, G its group of holomorphic diffeomorphisms. For a generic triple of points ( σ 1, σ 2, σ 3)∈ S× S× S, a characteristic G-invariant ι( σ 1, σ 2, σ 3), called the Maslov index was introduced in [Transform. Groups 6...

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Bibliographic Details
Published in:Journal of geometry and physics 2004, Vol.49 (1), p.21-51
Main Author: Clerc, Jean-Louis
Format: Article
Language:English
Subjects:
Clifford algebras
Hermitian symmetric space of tube-type
Lagrangian subspace
Maslov index
Mathematics
Representation Theory
Shilov boundary
Spinors
Triple index
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Summary:Let D be an irreducible Hermitian symmetric space of tube-type, S its Shilov boundary, G its group of holomorphic diffeomorphisms. For a generic triple of points ( σ 1, σ 2, σ 3)∈ S× S× S, a characteristic G-invariant ι( σ 1, σ 2, σ 3), called the Maslov index was introduced in [Transform. Groups 6 (2001) 303]. For D of classical type (i.e. for all cases except for the exceptional domain associated to Albert’s algebra), the definition of the Maslov index is extended to all triples, by using a holomorphic embedding of D into a Siegel disc, which corresponds to an embedding of S into a Lagrangian manifold. When D is the Lie ball, the extension of the definition is obtained through a realization of S in the Lagrangian manifold of a spinor space.
ISSN:0393-0440
1879-1662
DOI:10.1016/S0393-0440(03)00059-7