Jordan algebras, geometry of Hermitian symmetric spaces and non-commutative Hardy spaces

Details Jordan algebras, geometry of Hermitian symmetric spaces and non-commutative Hardy spaces Jordan algebras, geometry of Hermitian symmetric spaces and non-commutative Hardy spaces

2006-09-15

arxiv.org/abs/math/0609446v1

Seminar on Mathematical Scieences, Keio University 33 (2005) 1-70

Mathematics

Representation Theory

Scientific paper

These notes were written following lectures I had the pleasure of giving on this subject at Keio University, during November and December 2004. The first part is about new applications of Jordan algebras to the geometry of Hermitian symmetric spaces and to causal semi-simple symmetric spaces of Cayley type. The second part will present new contributions for studing (non commutative) Hardy spaces of holomorphic functions on Lie semi-groups which is a part of the so called Gelfand-Gindikin program.

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