Cones from quantum groups to tropical flag varieties

2019/11/26 by Xin Fang, Fang, Xin, Ghislain Fourier +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.AG #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.1911.11828

15 pages, v2: statement of Corollary 1 corrected

arxiv created 2019/12/04 · arxiv updated 2019/12/06

Abstract

We relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study of monomials in canonical bases, to K-theoretic cones for quiver representations, and to some maximal prime cones in tropical flag varieties.

Related

• Rectangle diagrams for the Lusztig cones of quantized enveloping algebras of type A
• Weighted PBW degenerations and tropical flag varieties
• The Lusztig cones of a quantized enveloping algebra of type A
• A classification of H-primes of quantum partial flag varieties
• Regions of linearity, Lusztig cones and canonical basis elements for the quantized enveloping algebra of type A₄