Parabolic character sheaves, I
By G.Lusztig. 2003
60 citations recorded by the source corpus.
0.1. Let G be a connected reductive algebraic group over an algebraically closed field k. Let Z be the variety (of the same dimension as G) consisting of all pairs (P, gUP ) where P runs through a fixed conjugacy class P of parabolics of G and gUP ∈ G/UP (UP is the unipotent radical of P ). Now G acts on Z by h : (P, gUP ) 7→ (hPh , hghUhPh−1). In this paper we study a class of simple G-equivariant perverse sheaves on Z which we call ”parabolic character sheaves”. In the case where P = {G}, these are the character sheaves on Z = G, in the sense of [L3]. In general, they have several common properties with the character sheaves: they are defined in arbitrary characteristic, and in the case where k is an algebraic closure of a finite field Fq and G,P are defined over Fq, (a) the characteristic functions of the parabolic character sheaves that are defined over Fq form a basis of the space of G(Fq)-invariant functions on Z(Fq) (under a mild assumption on the characteristic of k).
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6a6d1c7c958bb6521a3ca32a736d955b3ebbf38d
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the variety of Lagrangian subalgebras, II (2001, methodology): “The GΔorbits in the wonderful compactifications were also studied by Lusztig in [26] and [27] using a somewhat different method.”
- Stratifications in the reduction of Shimura varieties (2015, methodology): “Now we discuss the decomposition of K̆wK̆ into finitely many subsets stable under the action of K̆σ, analogous to the G-stable piece decomposition (for reductive groups G over algebraically closed fields) introduced by Lusztig in [35].”
- $F$-zips with additional structure (2012, background): “They showed that the isomorphism classes of F -zips of fixed dimension n and with a fixed type of Hodge filtration over an algebraically closed field are in natural bijection with the orbits under GLn,k in a variant Z ′ I of the varieties ZI studied by Lusztig [12], [13].”