Professor Dr. Jost-Hinrich Eschenburg
Montag, 20. November 2017
Raum 2004 (L1)
über das Thema:
|(The following is mainly work of my Ph.D. student Erich Dorner.) The compact irreducible symmetric spaces of type I (not groups) come in 7 infinite series ("classical spaces") and 12 single spaces ("exceptional spaces"). The classical spaces consists of the Grassmannians over the real, complex and quaternionic numbers and the various spaces of real, complex, quaternionic structures. All of them are related to linear algebra over the real, complex or quaternionic numbers. The exceptional spaces should belong "somehow" to the remaining normed division algebra, the octonion algebra. They allow a similar classification where the role of the Grassmannians is played by the four "Rosenfeld planes" of dimensions 16, 32, 64, 128, acted on by the exceptional groups F4, E6, E7, E8. It is the aim of the talk to construct and understand these spaces and their Dynkin diagrams in terms of the spin representation on T² where T denotes the tensor product of two normed division algebras. This is essentially the isotropy representation of a symmetric space which is classical (a Grassmannian) when both division algebras are associative. This fact greatly helps understanding the non-associative cases too.|
|Hierzu ergeht herzliche Einladung.|
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).