PBW degenerations, quiver Grassmannians, and toric varieties
Evgeny Feigin
TL;DR
This paper reviews the connections between PBW degenerations, quiver Grassmannians, and toric varieties, highlighting recent advances in understanding degenerations of flag varieties through Lie theory and representation theory.
Contribution
It synthesizes recent discoveries linking PBW degenerations, quiver Grassmannians, and toric varieties, providing a comprehensive overview of their interrelations.
Findings
PBW degenerations relate to quiver Grassmannians.
Flag varieties can degenerate into toric varieties.
Lie theory underpins the structure of these degenerations.
Abstract
We present a review on the recently discovered link between the Lie theory,the theory of quiver Grassmannians, and various degenerations of flag varieties. Our starting point is the induced Poincar\'{e}--Birkhoff--Witt filtration on the highest weight representations and the corresponding PBW degenerate flag varieties.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra