Beyond the Sottile–Sturmfels Degeneration of a Semi-Infinite Grassmannian

Evgeny Feigin, Igor Makhlin, Alexander Popkovich

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)10037-10066
Number of pages30
JournalInternational Mathematics Research Notices
Issue number12
StatePublished - 1 Jun 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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