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Representation Theory

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Microlocal characterization of Lusztig sheaves for affine quivers and $g$-loops quivers

Author: Lucien Hennecart
Journal: Represent. Theory 26 (2022), 17-67
MSC (2020): Primary 16G20
Published electronically: February 11, 2022
MathSciNet review: 4379987
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Abstract: We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig category are characterized by the nilpotency of their singular support. This proves a conjecture of Lusztig in the case of affine quivers. For cyclic quivers, we prove a similar result for a larger nilpotent variety and a larger class of perverse sheaves. We formulate conjectures concerning similar results for quivers with loops, for which we have to use the appropriate notion of nilpotent variety, due to Bozec, Schiffmann and Vasserot. We prove our conjecture for $g$-loops quivers ($g\geq 2$).

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Lucien Hennecart
Affiliation: Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay, France
MR Author ID: 1450534

Received by editor(s): October 9, 2020
Received by editor(s) in revised form: September 13, 2021
Published electronically: February 11, 2022
Article copyright: © Copyright 2022 American Mathematical Society