Floer cohomology of g-equivariant Lagrangian branes

Yankl Lekili, James Pascaleff

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)1071-1110
Number of pages40
JournalCompositio Mathematica
Issue number5
StatePublished - May 1 2016


  • equivariant Lagrangian branes
  • homological mirror symmetry
  • semisimple Lie algebras
  • symplectic cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Floer cohomology of g-equivariant Lagrangian branes'. Together they form a unique fingerprint.

Cite this