Some New Applications of the Schur-Sato Theory
Time: 2023-10-27
Published By: Wenqiong Li
Speaker(s): Alexander Zheglov (Lomonosov Moscow State University)
Time: 14:00-15:00 October 31, 2023
Venue: Room 29, Quan Zhai, BICMR
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.
