Abstract
Building on Seidel and Solomon's fundamental work [Symplectic cohomology and-intersection numbers, Geom. Funct. Anal. 22 (2012), 443-477], we define the notion of a-equivariant Lagrangian brane in an exact symplectic manifold, where is a sub-Lie algebra of the symplectic cohomology of. When is a (symplectic) mirror to an (algebraic) homogeneous space, homological mirror symmetry predicts that there is an embedding of in. This allows us to study a mirror theory to classical constructions of Borel, Weil and Bott. We give explicit computations recovering all finite-dimensional irreducible representations of as representations on the Floer cohomology of an-equivariant Lagrangian brane and discuss generalizations to arbitrary finite-dimensional semisimple Lie algebras.
Original language | English (US) |
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Pages (from-to) | 1071-1110 |
Number of pages | 40 |
Journal | Compositio Mathematica |
Volume | 152 |
Issue number | 5 |
DOIs | |
State | Published - May 1 2016 |
Keywords
- equivariant Lagrangian branes
- homological mirror symmetry
- semisimple Lie algebras
- symplectic cohomology
ASJC Scopus subject areas
- Algebra and Number Theory