On Two Notions of Total Positivity for Generalized Partial Flag Varieties of Classical Lie Types

International Mathematics Research Notices 2026 Open access

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Authors: Grant T. Barkley, Jonathan Boretsky, Christopher Eur, Jiyang Gao
DOI: 10.1093/imrn/rnag012
Cited by: 0
References: 29

Abstract

Abstract For Grassmannians, Lusztig’s notion of total positivity coincides with positivity of the Plücker coordinates. This coincidence underpins the rich interaction between matroid theory, tropical geometry, and the theory of total positivity. Bloch and Karp furthermore characterized the (type A) partial flag varieties for which the two notions of positivity similarly coincide. We characterize the symplectic (type C) and odd-orthogonal (type B) partial flag varieties for which Lusztig’s total positivity coincides with Plücker positivity.

Fields of Study & Subjects

Advanced Combinatorial Mathematics Advanced Algebra and Geometry Algebraic Geometry and Number Theory

Publication details

Journal / source
International Mathematics Research Notices
Volume
2026
Issue
3
Publication date
15 January 2026
Language
EN