On toric degenerations of flag varieties
Xin Fang, Ghislain Fourier, Peter Littelmann
TL;DR
This paper explores methods for toric degenerations of flag varieties using advanced algebraic geometry and representation theory tools, aiming to deepen understanding of their structure and degenerations.
Contribution
It integrates canonical bases, Newton-Okounkov bodies, PBW-filtrations, and cluster algebras to advance the study of toric degenerations of flag varieties.
Findings
Unified framework for toric degenerations
Application of cluster algebras to flag varieties
Enhanced understanding of geometric structures
Abstract
Following the historical track in pursuing -equivariant flat toric degenerations of flag varieties and spherical varieties, we explain how powerful tools in algebraic geometry and representation theory, such as canonical bases, Newton-Okounkov bodies, PBW-filtrations and cluster algebras come to push the subject forward.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Combinatorial Mathematics · Algebraic Geometry and Number Theory