Cones from quantum groups to tropical flag varieties
Xin Fang, Ghislain Fourier, Markus Reineke
TL;DR
This paper explores the connections between quantum degree cones, Lusztig's cones, K-theoretic cones, and tropical flag varieties, revealing deep relationships across quantum groups, algebraic geometry, and combinatorics.
Contribution
It establishes new links between quantum degree cones and tropical flag varieties, integrating concepts from quantum groups, canonical bases, and tropical geometry.
Findings
Quantum degree cones relate to Lusztig's cones and K-theoretic cones.
Identifies maximal prime cones in tropical flag varieties.
Bridges quantum algebra and tropical geometry through cone structures.
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Combinatorial Mathematics