Year: 2024
Type: preprint
Abstract: We systematically study the commutative factorization categories over the Ran space. We fill in what we consider as a gap in the construction of the factorizable Satake functor in the constructible setting in arXiv:1708.07205, arXiv:1608.00284. To do so, we summarize four different constructions of commutative factorization sheaves of categories on Ran and establish some relations between them. We also generalize the Drinfeld-Plücker formalism from arXiv:1708.07205, arXiv:2310.0638. In addition, we study the commutative factorization categories Fact(C) with an additional grading of C. We apply our results to relate the versions of the Satake functors for the Ran space with that of the configuration space of colored divisors on a curve. This paper is a companion of arXiv:2508.01527.
Source: arXiv (Cornell University)
Author: Lysenko, Sergey
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394948230