EVENT DETAILS AND ABSTRACT

Title: Equivariant Lagrangian branes and Representations
Speaker: Yanki Lekili
Speaker Info: UIC
Brief Description:
Special Note:
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 (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.