Conjugacy classes of \(n\)-tuples in semi-simple Jordan algebras
Friday, 5.12.14, 10:15-11:15, Raum 404, Eckerstr. 1
Let \(J\) be a (complex) semi-simple Jordan algebra, and consider the action of the automorphism group acts\non the \(n\)-fold product of \(J\) via the diagonal action. In the talk, geometric properties of this action\nare studied. In particular, a characterization of the closed orbits is given.\n\nIn the case of a complex reductive linear algebraic group and the adjoint action on the \(n\)-fold product\nof its Lie algebra, a result of R.W. Richardson characterizes the closed orbits. A similar condition can\nbe found in the case of Jordan algebras. It turns out that the orbit through an \(n\)-tuple \(x=(x_1,\bldots, x_n)\)\nis closed if and only if the Jordan subalgebra generated by \(x_1,\bldots, x_n\) is semi-simple.\n\nFor the proof, the existence of certain one-parameter subgroups of the automorphism group is important. Those\none-parameter subgroups have special properties with respect to a given subalgebra of the Jordan algebra \(J\).
On automorphic forms for Calabi-Yau threefolds
Friday, 12.12.14, 10:15-11:15, Raum 404, Eckerstr. 1
I will present a novel approach to relate Hodge theory of elliptic curves to quasimodular forms. Then we consider its generalization to the Hodge theory of Calabi-Yau threefolds, leading to the appearance of a new family of Lie algebras.
Walled Brauer algebra and higher Schur-Weyl duality
Friday, 19.12.14, 10:15-11:15, Raum 404, Eckerstr. 1