Pure and Applied Mathematics Quarterly

Volume 13 (2017)

Number 2

Special Issue in Honor of Yuri Manin: Part 2 of 2

Guest Editors: Lizhen Ji, Kefeng Liu, Yuri Tschinkel, and Shing-Tung Yau

Wall-crossing functors for quantized symplectic resolutions: perversity and partial Ringel dualities

Pages: 247 – 289

DOI: https://dx.doi.org/10.4310/PAMQ.2017.v13.n2.a3


Ivan Losev (Department of Mathematics, Northeastern University, Boston, Massachusetts, U.S.A.; and the International Laboratory of Representation Theory & Mathematical Physics, NRU-HSE, Moscow, Russia)


In this paper we study wall-crossing functors between categories of modules over quantizations of symplectic resolutions. We prove that wall-crossing functors through faces are perverse equivalences and use this to verify an Etingof type conjecture for quantizations of Nakajima quiver varieties associated to affine quivers. In the case when there is a Hamiltonian torus action on the resolution with finitely many fixed points so that it makes sense to speak about categories $\mathcal{O}$ over quantizations, we introduce new standardly stratified structures on these categories $\mathcal{O}$ and relate the wall-crossing functors to the Ringel duality functors associated to these standardly stratified structures.

2010 Mathematics Subject Classification

Primary 16G99. Secondary 16G20, 53D20, 53D55.

Received 20 August 2017

Published 14 September 2018