75 citations · 305 across the 41 of their papers we have counts for
39 papers · 1 filter
Linear degenerate symplectic flag varieties: symmetric degenerations and PBW locus
Magdalena Boos, Giovanni Cerulli Irelli, Xin Fang +1
We conceptualize in the paper the linear degenerate symplectic flag varieties as symmetric degenerations within the framework of type equioriented quivers. First, in the larger…
Dynkin abelianisations of flag varieties
Shreepranav Varma Enugandla, Xin Fang, Ghislain Fourier +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 parameter…
Computing monomial bases in Lie theory using OSCAR
Xin Fang, Ghislain Fourier, Lars Göttgens +1
In this survey, we present a detailed guide on using the computer algebra system OSCAR to compute monomial bases for simple, finite-dimensional modules of simple, complex Lie algeb…
FFLV polytopes are string polytopes
Ester Cleusters, Ghislain Fourier, Felix Lerner
In this paper, we establish that FFLV polytopes, which describe monomial bases compatible with the PBW filtration on finite-dimensional simple modules for $\lie{sl}_n$ and $\lie{sp…
A minimal Gröbner basis for simple - or -modules
Ghislain Fourier, León van Eß
We explicitly provide minimal Gröbner bases for simple, finite-dimensional modules of complex Lie algebras of types A and C, using a homogeneous ordering that is compatible with th…
Specialization map for quiver Grassmannians
Giovanni Cerulli Irelli, Francesco Esposito, Xin Fang +1
We define a specialization map between cohomology algebras of quiver Grassmannians of Dynkin type and we prove that it is surjective in type A. This generalizes a result of Lanini…