Algebraic zip data
Richard Pink, Torsten Wedhorn, Paul Ziegler

TL;DR
This paper introduces algebraic zip data involving reductive groups and parabolic subgroups, studies the group actions and stratifications on the group, and connects these structures to known geometric objects like Lusztig's G-stable pieces and F-zip classifications.
Contribution
It generalizes the theory of algebraic zip data, describes the stratification and stabilizers of the group action, and links these to important geometric structures in representation theory and algebraic geometry.
Findings
Defined smooth E-invariant subvarieties and their stratification of G
Determined dimensions, closures, and stabilizers of these subvarieties
Connected algebraic quotients to Lusztig's G-stable pieces and F-zip classifications
Abstract
An algebraic zip datum is a tuple consisting of a reductive group together with parabolic subgroups and and an isogeny . We study the action of the group on given by . We define certain smooth -invariant subvarieties of , show that they define a stratification of . We determine their dimensions and their closures and give a description of the stabilizers of the -action on . We also generalize all results to non-connected groups. We show that for special choices of the algebraic quotient stack is isomorphic to or to , where is a -variety studied by Lusztig and He in the theory of character sheaves on spherical compactifications of and where has…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models
