The Thickness of Schubert Cells as Incidence Structures

John Bamberg, Arun Ram, Jon Xu

Research output: Contribution to journalArticle

Abstract

This paper explores the possible use of Schubert cells and Schubert varieties in finite geometry, particularly in regard to the question of whether these objects might be a source of understanding of ovoids or provide new examples. The main result provides a characterization of those Schubert cells for finite Chevalley groups which have the first property (thinness) of ovoids. More importantly, perhaps this short paper can help to bridge the modern language barrier between finite geometry and representation theory. For this purpose, this paper includes very brief surveys of the powerful lattice theory point of view from finite geometry and the powerful method of indexing points of flag varieties by Chevalley generators from representation theory.

Original languageEnglish
Pages (from-to)145-156
Number of pages12
JournalJournal of the Australian Mathematical Society
Volume109
Issue number2
DOIs
Publication statusPublished - Oct 2020

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