A Landau-Ginzburg model for Lagrangian Grassmannians, Langlands duality and relations in quantum cohomology

Pech, Clelia and Rietsch, Konstanze (2014) A Landau-Ginzburg model for Lagrangian Grassmannians, Langlands duality and relations in quantum cohomology. arXiv, . arXiv:1304.4958 [math.AG]. (Unpublished) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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Abstract

In [Rie08], the second author defined a Landau-Ginzburg model for homogeneous spaces G/P, as a regular function on an affine subvariety of the Langlands dual group. In this paper, we reformulate this LG-model (X^,W_t) in the case of the Lagrangian Grassmannian LG(m) as a rational function on a Langlands dual orthogonal Grassmannian, in the spirit of work by R. Marsh and the second author [MR12] for type A Grassmannians. This LG model has some very interesting features, which are not visible in the type A case, to do with the non-triviality of Langlands duality. We also formulate a conjecture relating our superpotential with the quantum differential equations of LG(m). Finally, our expression for W_t also leads us to conjecture new formulas in the quantum Schubert calculus of LG(m).

Item Type: Article
Uncontrolled keywords: mirror symmetry; Lagrangian Grassmannians; Langlands duality; quantum cohomology.
Subjects: Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory
Q Science > QA Mathematics (inc Computing science) > QA564 Algebraic Geometry
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Clelia Pech
Date Deposited: 21 Oct 2015 10:25 UTC
Last Modified: 08 May 2018 08:56 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51112 (The current URI for this page, for reference purposes)
Pech, Clelia: https://orcid.org/0000-0001-6142-6679
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