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arXiv · 2110.07397

Beyond the Sottile-Sturmfels degeneration of a semi-infinite Grassmannian

Evgeny Feigin·Igor Makhlin·Alexander Popkovich
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Abstract

We study toric degenerations of semi-infinite Grassmannians (a.k.a. quantum Grassmannians). While the toric degenerations of the classical Grassmannians are well studied, the only known example in the semi-infinite case is due to Sottile-Sturmfels. We start by providing a new interpretation of the Sottile-Sturmfels construction by finding a poset such that their degeneration is the toric variety of the order polytope of the poset. We then use our poset to construct and study a new toric degeneration in the semi-infinite case. Our construction is based on the notion of poset polytopes introduced by Fang-Fourier-Litza-Pegel. As an application we introduce semi-infinite PBW-semistandard tableaux, giving a basis in the homogeneous coordinate ring of a semi-infinite Grassmannian.

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Evgeny Feigin, Igor Makhlin, Alexander Popkovich. 2021-10-14. Beyond the Sottile-Sturmfels degeneration of a semi-infinite Grassmannian. https://arxiv.org/abs/2110.07397

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