Structure of Clifford algebras of isotropy representations associated to symmetric pairs (Andrey Krutov, Prague & Karmen Grizelj, Zagreb)

05.12.2023 15:00 – 17:15

Let (g,k) be a symmetric pair and p be the corresponding isotropy representation of k, namely, g = k \oplus p. Let h be a Cartan subalgebra of g such that t := k \cap h is a Cartan subalgebra of k. Set a := h \cap p. Assume that g admits a non-degenerate symmetric bilinear form B. Then the restrictions of B to k and p are also non-degenerate which allows us to consider the Clifford algebra Cl(p) of the isotropy representation. One can show that the subalgebra of k-invariants in Cl(p) is isomophic to the tensor product of the Clifford algebra Cl(a) and the characteristic subalgebra A. In the first talk we will discuss the structure of the algebra A. In the second talk we will discuss properties of Cl(a).
This is joint work with K. Calvert and P. Pandžić.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre