Beyond the Sottile–Sturmfels Degeneration of a Semi-Infinite Grassmannian
| Autor: | Evgeny Feigin, Igor Makhlin, Alexander Popkovich |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | International Mathematics Research Notices. |
| ISSN: | 1687-0247 1073-7928 |
| Popis: | 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 and 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. |
| Databáze: | OpenAIRE |
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