nLab factorizable sheaf

Idea

Factorizable sheaves are (typically constructible or perverse) sheaves equipped with certain factorization isomorphisms satisfying some associativity (coherence).

Related items

Related notions in $n$Lab include factorization algebra, factorization homology

First instance of such a factorization isomorphism has been observed by George Wilson in the context of Calogero-Moser space?,

• George Wilson, Collisions of Calogero-Moser particles and an adelic Grassmannian, With an appendix by I. G. Macdonald. Invent. Math. 133:1 (1998) 1–41 MR99f:58107, doi

Appearance in the context of quantum groups and in a relation to Kazhdan-Lusztig correspondence? is studied in

• Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman, Factorizable sheaves and quantum groups, Springer 2006 gBooks

• Dennis Gaitsgory, Notes on factorizable sheaves, pdf

• Gwyn Bellamy, Factorization in generalized Calogero–Moser spaces, Journal of Algebra 321:1 (2009) 338–344

Using a recent construction of Bezrukavnikov and Etingof, (R. Bezrukavnikov, P. Etingof, Induction and restriction functors for rational Cherednik algebras, arXiv:0803.3639), we prove that there is a factorization of the Etingof–Ginzburg sheaf on the generalized Calogero–Moser space associated to a complex reflection group. In the case, this confirms a conjecture of Etingof and Ginzburg (P. Etingof, V. Ginzburg, Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphisms, Invent. Math 147 (2002) 243–348)

• James Tao, Yifei Zhao, Extensions by K2 and factorization line bundles, arXiv:1901.08760
• Vadim Schechtman, Fourier-Sato transform, braid group actions, and factorizable sheaves, 2014 slides pdf