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Perverse sheaves on the nilpotent cone and Lusztig’s generalized Springer correspondence. (English) Zbl 1427.17009

Misra, Kailash C. (ed.) et al., Lie algebras, Lie superalgebras, vertex algebras and related topics. 2012–2014 Southeastern Lie theory workshop series: Categorification of quantum groups and representation theory, North Carolina State University, Raleigh, NC, USA, April 21–22, 2012. Lie algebras, vertex algebras, integrable systems and applications, College of Charleston, Charleston, SC, USA, December 16–18, 2012. Noncommutative algebraic geometry and representation theory, Louisiana State University, Baton Rouge, LA, USA, May 10–12, 2013. Representation theory of Lie algebras and superalgebras, University of Georgia, Athens, GA, USA, May 16–17, 2014. Proceedings. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 92, 273-292 (2016).
Summary: In this note, we consider perverse sheaves on the nilpotent cone. We prove orthogonality relations for the equivariant category of sheaves on the nilpotent cone in a method similar to Lusztig’s for character sheaves. We also consider cleanness for cuspidal perverse sheaves and the generalized Lusztig-Shoji algorithm.
For the entire collection see [Zbl 1343.17001].

MSC:

17B08 Coadjoint orbits; nilpotent varieties
20G05 Representation theory for linear algebraic groups
14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
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