Event Details

Speaker: Kieran Calvert (Lancaster) Title: Clifford algebra invariants of symmetric pairs and Schur polynomials

Abstract: Let (g,k) be a symmetric pair of reductive Lie algebras, then g is a direct sum of k and p. Using the Killing form, one can construct the Clifford algebra associated to p. In this talk I will discuss the k invariant subalgebra of this Clifford algebra. The related associated graded algebra is a model for the de Rham cohomology of the symmetric space G/K. A description of the Clifford algebra gives a deformed analogue of the cohomology which reveals a conceptually cleaner method to calculate the cohomology of G/K. In particular, for G/K diffeomorphic to a Grassmannian manifold, I will demonstrate a novel way to calculate the product of Schur polynomials. This is joint work with Andrey Krutov, Kyo Nishiyama and Pavle Pandžić.