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

Year: 2026

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnag012

Authors: Grant Barkley, Jonathan Boretsky, Christopher Eur, Jiyang Gao

Institutions: University of Michigan, McGill University, Carnegie Mellon University, Harvard University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

OpenAlex ID: W7128396368

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Cites: 29

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