Some New Applications of the Schur-Sato Theory
发布时间：2023年10月27日
浏览次数：1854
发布者: Wenqiong Li
主讲人： Alexander Zheglov (Lomonosov Moscow State University)
活动时间： 从 2023-10-31 14:00 到 15:00
场地： 北京国际数学研究中心，全斋全29教室
The Schur-Sato theory, which will be discussed in the talk, is a generalization of a well-known theory in dimension one, where it describes rings of ordinary differential operators in terms of points of the big cell of Sato grassmanian. This theory was developed for a wide class of so-called quasi-elliptic rings in arbitrary dimension in the work https://arxiv.org/abs/2205.06790. Such rings have been defined in order to classify a wide class of commutative rings of operators appeared in the theory of (quantum) integrable systems (such as, for example, rings of commuting differential, difference, differential-difference and etc. operators). The theory was applied to get classification of quasi-elliptic rings in terms of some subspaces (generalized Schur pairs). I’ll talk about a new application of the theory: a convenient description of the moduli space of spectral sheaves of quasi-elliptic rings. This moduli space is an open set of the moduli space of torsion free sheaves with fixed Hilbert polynomial on the spectral variety.
