Derivation functors and Lusztig's induction functors
Minghui Zhao
TL;DR
This paper explores the relationship between induction and derivation functors within the framework of Lusztig's perverse sheaves, building on previous work to deepen understanding of their compatibility and categorification.
Contribution
It introduces a new study of the relation between induction and derivation functors, extending the categorification of Green's formula to this context.
Findings
Established a connection between induction and derivation functors.
Extended categorification of Green's formula to include derivation functors.
Provided a sheaf-level proof of compatibility for all semisimple complexes.
Abstract
Lusztig proved the compatibility of induction functors and restriction functors for Lusztig's perverse sheaves. Fang-Lan-Xiao established a categorification of Green's formula and gave a sheaf-level proof of this compatibility for all semisimple complexes. As an application, we study the relation between induction functors and derivation functors, which is a kind of special restriction functors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory