Shreepranav Varma Enugandla, Xin Fang, Ghislain Fourier, Christian Steinert
Published 2024-04-08Version 1
Cerulli Irelli and Lanini have shown that PBW degenerations of flag varieties in type A and C are actually Schubert varieties of higher rank. We introduce Dynkin cones to parameterise specific abelianisations of classical Lie algebras. Within this framework, we generalise their result to all degenerations of flag varieties defined by degree vectors originating from a Dynkin cone. This framework allows us to determine the extent to which a flag variety can be degenerate while still naturally being a Schubert variety of the same Lie type. Furthermore, we compute the defining relations for the corresponding degenerate simple modules in all classical types.
Comments: 27 pages, this is a preliminary version
String cone and Superpotential combinatorics for flag and Schubert varieties in type A
The Poisson degeneracy locus of a flag variety
$B_{n-1}$-orbits on the flag variety and the Bruhat graph for $S_{n}\times S_{n}$
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