21 citations · 95 across the 33 of their papers we have counts for
39 papers
Extriangulated ideal quotients, with applications to cluster theory and gentle algebras
Xin Fang, Mikhail Gorsky, Yann Palu +2
We extend results of Brüstle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpre…
Tropical symplectic flag varieties: a Lie-theoretic approach
George Balla, Xin Fang
We study tropicalization of symplectic flag varieties with respect to the Plücker embedding. We identify a particular maximal prime cone in this tropicalization by explicitly givin…
Seshadri stratifications and Schubert varieties: a geometric construction of a standard monomial theory
Rocco Chirivì, Xin Fang, Peter Littelmann
A standard monomial theory for Schubert varieties is constructed exploiting (1) the geometry of the Seshadri stratifications of Schubert varieties by their Schubert subvarieties an…
On normal Seshadri stratifications
Rocco Chirivì, Xin Fang, Peter Littelmann
The existence of a Seshadri stratification on an embedded projective variety provides a flat degeneration of the variety to a union of projective toric varieties, called a semi-tor…
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…
LS Algebras, Valuations and Schubert Varieties
Rocco Chirivì, Xin Fang, Peter Littelmann
In this paper, we propose an algebraic approach via Lakshmibai-Seshadri (LS) algebras to establish a link between standard monomial theories, Newton-Okounkov bodies and valuations.…
Seshadri stratification for Schubert varieties and Standard Monomial Theory
Rocco Chirivì, Xin Fang, Peter Littelmann
The theory of Seshadri stratifications has been developed by the authors with the intention to build up a new geometric approach towards a standard monomial theory for embedded pro…
Seshadri stratifications and standard monomial theory
Rocco Chirivì, Xin Fang, Peter Littelmann
We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat deg…
Exact structures and degeneration of Hall algebras
Xin Fang, Mikhail Gorsky
We study degenerations of the Hall algebras of exact categories induced by degree functions on the set of isomorphism classes of indecomposable objects. We prove that each such deg…
Lusztig polytopes and FFLV polytopes
Xin Fang, Gleb Koshevoy
In this paper we prove that in type , the Feigin-Fourier-Littelmann-Vinberg (FFLV) polytope coincides with the Minkowski sum of Lusztig polytopes arising from various redu…
Cones from quantum groups to tropical flag varieties
Xin Fang, Ghislain Fourier, Markus Reineke
We relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study of monomials…
Linear degenerations of flag varieties: partial flags, defining equations, and group actions
Giovanni Cerulli Irelli, Xin Fang, Evgeny Feigin +2
We continue, generalize and expand our study of linear degenerations of flag varieties from [G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier, M. Reineke, Math. Z. 287 (2017), no.…
On -distance-transitive graphs
Hui Zhou, Cheryl Praeger, Michael Giudici +2
Distance-regular graphs have many beautiful combinatorial properties. Distance-transitive graphs have very strong symmetries, and they are distance-regular, i.e. distance-transitiv…
Degenerate Schubert Varieties in Type A
Rocco Chirivi', Xin Fang, Ghislain Fourier
We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated to a rectangular…
The Minkowski Property and Reflexivity of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Christoph Pegel
We provide a Minkowski sum decomposition of marked chain-order polytopes into building blocks associated to elementary markings and thus give an explicit minimal set of generators…
Supports for linear degenerations of flag varieties
Xin Fang, Markus Reineke
We determine the set of supports for the flat family of linear degenerations of flag varieties in terms of Motzkin combinatorics.
Symmetries on plabic graphs and associated polytopes
Xin Fang, Ghislain Fourier
For Grassmann varieties, we explain how the duality between the Gelfand-Tsetlin polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes arises from different positive structu…
A Continuous Family of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Jan-Philipp Litza +1
For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing tran…
Weighted PBW degenerations and tropical flag varieties
Xin Fang, Evgeny Feigin, Ghislain Fourier +1
We study algebraic, combinatorial and geometric aspects of weighted PBW-type degenerations of (partial) flag varieties in type . These degenerations are labeled by degree functi…
From standard monomial theory to semi-toric degenerations via Newton-Okounkov bodies
Xin Fang, Peter Littelmann
The Hodge algebra structures on the homogeneous coordinate rings of Grassmann varieties provide semi-toric degenerations of these varieties. In this paper we construct these semi-t…
Toric degenerations of Gr(2,n) and Gr(3,6) via plabic graphs
Lara Bossinger, Xin Fang, Ghislain Fourier +2
We establish an explicit bijection between the toric degenerations of the Grassmannian arising from maximal cones in tropical Grassmannians and the ones coming f…
On toric degenerations of flag varieties
Xin Fang, Ghislain Fourier, Peter Littelmann
Following the historical track in pursuing -equivariant flat toric degenerations of flag varieties and spherical varieties, we explain how powerful tools in algebraic geometry a…
Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint orbits
Xin Fang, Peter Littelmann, Milena Pabiniak
We give a uniform proof for the conjectured Gromov width of coadjoint orbits of all compact connected simple Lie groups, by analyzing simplices in Newton-Okounkov bodies.
Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras
Xin Fang
In this paper generalized Matsumoto-Tits sections lifting permutations to the algebra associated to a generalized virtual braid monoid are defined. They are then applied to study t…