Type: Seminar

Distribution: World

Expiry: 23 Oct 2017

CalTitle1: Algebra Seminar: On equations defining the affine Grassmannian of SL_n

Auth: kevinc@120.88.165.116 (kcou7211) in SMS-WASM

Oded Yacobi (University of Sydney) Friday 22 September, 12-1pm, Place: Carslaw 375 Title: On equations defining the affine Grassmannian of SL_n Abstract: The affine Grassmannian Gr of a semisimple group G is an important infinite dimensional variety that appears in representation theory. This talk concerns the projective geometry of the affine Grassmannian when G=SL_n. More precisely, in this case Gr naturally embeds into the Sato Grassmannian SGr, which is a limit of finite dimensional Grassmannians Gr(n,2n) as n --> infinity, and we are interested in the equations defining the embedding Gr < SGr. Kreiman, Lakshmibai, Magyar and Weyman constructed linear equations on SGr which vanish on Gr and conjectured that these equations suffice to cut out the affine Grassmannian. We recently proved this conjecture by reducing it to a question about finite dimensional Grassmannians. I’ll describe our method of proof and time permitting I’ll mention some conjectures (in both the finite and infinite dimensional settings) that arise from our work, and also some potential applications. This is joint work with Dinakar Muthiah and Alex Weekes