Canonical bases in Lie theory and total positivity

2025/08/03 by G. Lusztig, Lusztig, G.
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2508.01795

openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This represents a talk given at the International Conference for Basic Science, July 2025. We review the theory of canonical bases of quantum groups and its relation with the theory of total positivity.

Citations

• Canonical bases via pairing monomials
• From Weyl groups to semisimple groups
• Unzerlegbare Darstellungen I

Related

• Positivity properties for canonical bases of modified quantum affine \fraksl_n
• Positivity properties of canonical bases
• Positivity of Canonical Bases under Comultiplication
• From Weyl groups to semisimple groups
• A survey of total positivity