Loading...
Please wait, while we are loading the content...
Similar Documents
Floer cohomology of -equivariant Lagrangian branes
| Content Provider | Scilit |
|---|---|
| Author | Lekili, Yankı Pascaleff, James |
| Copyright Year | 2015 |
| Description | Journal: Compositio Mathematica Building on Seidel and Solomon’s fundamental work [Symplectic cohomology and $q$ -intersection numbers, Geom. Funct. Anal. 22 (2012), 443–477], we define the notion of a $\mathfrak{g}$ -equivariant Lagrangian brane in an exact symplectic manifold $M$ , where $\mathfrak{g}\subset SH^{1}(M)$ is a sub-Lie algebra of the symplectic cohomology of $M$ . When $M$ is a (symplectic) mirror to an (algebraic) homogeneous space $G/P$ , homological mirror symmetry predicts that there is an embedding of $\mathfrak{g}$ in $SH^{1}(M)$ . 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 $\mathfrak{sl}_{2}$ as representations on the Floer cohomology of an $\mathfrak{sl}_{2}$ -equivariant Lagrangian brane and discuss generalizations to arbitrary finite-dimensional semisimple Lie algebras. |
| Ending Page | 1110 |
| Starting Page | 1071 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x1500771x |
| Journal | Compositio Mathematica |
| Issue Number | 5 |
| Volume Number | 152 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2015-12-17 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Mathematical Physics Homological Mirror Symmetry |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
