Floer cohomology of -equivariant Lagrangian branes
| Autor: | James Pascaleff, Yanki Lekili |
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| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Homological mirror symmetry 010102 general mathematics Mathematics::Algebraic Topology 01 natural sciences Cohomology Mathematics::K-Theory and Homology Irreducible representation 0103 physical sciences Lie algebra Equivariant map 010307 mathematical physics 0101 mathematics Brane Mathematics::Symplectic Geometry Mathematics Symplectic manifold Symplectic geometry |
| Zdroj: | Lekili, Y & Pascaleff, J 2016, ' Floer cohomology of g-equivariant Lagrangian branes ', COMPOSITIO MATHEMATICA, vol. 152, pp. 1071-1110 . https://doi.org/10.1112/S0010437X1500771X |
| ISSN: | 1570-5846 0010-437X |
| DOI: | 10.1112/s0010437x1500771x |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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