Geometry, Topology and Dynamics Seminar
Yank\i\ Lekili
UIC
Equivariant Lagrangian branes and Representations
Abstract: Classical Bott-Borel-Weil theory constructs irreducible representations of semisimple Lie algebras on the section spaces of
homogeneous vector bundles on homogeneous spaces. In this talk, we decribe a construction in symplectic geometry which is meant to serve
as the mirror dual to Bott-Borel-Weil construction. Building on Seidel-Solomon's fundamental work, we define the notion of
an "equivariant Lagrangian brane" in an exact symplectic manifold $M$ (which is meant to be the mirror dual of a homogenous variety $G/P$),
and construct representations of the Lie algebra $g=$Lie$G$, on Floer
cohomology of equivariant Lagrangian branes. We will make our construction completely explicit in the case of $sl_2$ and comment on
generalizations to arbitrary semisimple Lie algebras. This is a joint work with James Pascaleff.
Monday September 15, 2014 at 3:00 PM in SEO 636