adv

Fukaya category of Grassmannians: rectangles. (arXiv:1808.02955v1 [math.SG])

We show that the monotone Lagrangian torus fiber of the Gelfand-Cetlin integrable system on the complex Grassmannian $\operatorname{Gr}(k,n)$ supports generators for all maximum modulus summands in the spectral decomposition of the Fukaya category over $\mathbb{C}$, generalizing the example of the Clifford torus in projective space. We introduce an action of the dihedral group $D_n$ on the Landau-Ginzburg mirror proposed by Marsh-Rietsch that makes it equivariant and use it to show that, given a lower modulus, the torus supports nonzero objects in none or many summands of the Fukaya category with that modulus. The alternative is controlled by the vanishing of rectangular Schur polynomials at the $n$-th roots of unity, and for $n=p$ prime this suffices to give a complete set of generators and prove homological mirror symmetry for $\operatorname{Gr}(k,p)$.查看全文

Solidot 文章翻译

你的名字

留空匿名提交
你的Email或网站

用户可以联系你
标题

简单描述
内容