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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Microlocal characterization of Lusztig sheaves for affine quivers and $g$-loops quivers
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by Lucien Hennecart PDF
Represent. Theory 26 (2022), 17-67 Request permission


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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Additional Information
  • Lucien Hennecart
  • Affiliation: Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay, France
  • MR Author ID: 1450534
  • Email:
  • Received by editor(s): October 9, 2020
  • Received by editor(s) in revised form: September 13, 2021
  • Published electronically: February 11, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 17-67
  • MSC (2020): Primary 16G20
  • DOI:
  • MathSciNet review: 4379987