6 papers
Two remarks on decomposition numbers of standard modules for quantum affine
Xin Fang, Deniz Kus, Markus Reineke
We use Nakajima's geometric approach to representations of quantum affine algebras and recent results on explicit descriptions of specific canonical basis elements, to derive close…
Local intersection cohomology of varieties of complexes
Xin Fang, Markus Reineke
We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit construct…
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…
A Graphical Approach to the Frobenius Number Problem in Three Variables
Xinxin Fang
The Frobenius number for a set of relatively prime positive integers, where the smallest integer in the set is at least 2, is the largest integer that cannot be expressed as a nonn…