2013/04/17 by Clélia Pech, Pech, C., Konstanze Rietsch +1
Mathematics · #14J33 #14M17 #14N35 #20G20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1304.4958
openalex publication_date 2013/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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^,Wt) 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 Wt also leads us to conjecture new formulas in the quantum Schubert calculus of LG(m).