author={Rocco Chirivi' and Xin Gui Fang and Ghislain Fourier},
  journal={arXiv: Representation Theory},
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 element is indeed a Schubert variety in a partial flag variety of the same type with larger rank. Moreover, the degenerate Demazure module associated to a rectangular element is isomorphic to the Demazure module for this particular Schubert variety of larger rank. This generalizes previous results by Cerulli Irelli… Expand
3 Citations
PBW Degenerate Schubert Varieties: Cartan Components and Counterexamples
In recent years PBW degenerations of Demazure modules and Schubert varieties were defined and studied in several papers. Various interesting properties were obtained in type $\mathrm A$ but only withExpand
Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations
Consider a lattice of n sites arranged around a ring, with the n sites occupied by particles of weights {1,2, . . . , n}; the possible arrangements of particles in sites thus corresponds to the n!Expand
Consider a lattice of n sites arranged around a ring, with the n sites occupied by particles of weights {1,2, . . . , n}; the possible arrangements of particles in sites thus corresponds to the n!Expand


Following Schubert varieties under Feigin's degeneration of the flag variety
We describe the effect of Feigin's flat degeneration of the type $\textrm{A}$ flag variety on its Schubert varieties. In particular, we study when they stay irreducible and in several cases we areExpand
Linear degenerations of flag varieties
Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians. For type A flag varieties, we obtain characterizations of flatness, irreducibility and normality of theseExpand
Degenerate flag varieties and Schubert varieties: a characteristic free approach
We consider the PBW filtrations over the integers of the irreducible highest weight modules in type A and C. We show that the associated graded modules can be realized as Demazure modules for groupExpand
PBW-degenerated Demazure modules and Schubert varieties for triangular elements
  • G. Fourier
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 2016
These faces are normal polytopes and their Minkowski sum is compatible with tensor products, which implies that flat degenerations of the corresponding Schubert varieties to PBW degenerated and toric varieties are obtained. Expand
Deformation and Cohen-Macaulayness of the multicone over the flag variety
Abstract. A general theory of LS algebras over a multiposet is developed. As a main result, the existence of a flat deformation to discrete algebras is obtained. This is applied to the multicone overExpand
Degenerate flag varieties of type A and C are Schubert varieties
We show that in type A or C any degenerate flag variety is in fact isomorphic to a Schubert variety in an appropriate partial flag manifold.
Quiver Grassmannians and degenerate flag varieties
Quiver Grassmannians are varieties parametrizing subrepresentations of a quiver representation. It is observed that certain quiver Grassmannians for type A quivers are isomorphic to the degenerateExpand
Combinatorics of hypergeometric functions associated with positive roots
In this paper we study the hypergeometric system on unipotent matrices. This system gives a holonomic D-module. We find the number of independent solutions of this system at a generic point. ThisExpand
Multi-cones over Schubert varieties
Let ~q~ 1 . . . . , 2 ' , be invertible sheaves on a variety X. We may form the multigraded ring A = ~F(X, | where the vector (m) ranges in N". Then C = Spec(A) is a multi-cone. If X is a projectiveExpand
Degenerate flag varieties and the median Genocchi numbers
We study the $\bG_a^M$ degenerations $\Fl^a_\la$ of the type $A$ flag varieties $\Fl_\la$. We describe these degenerations explicitly as subvarieties in the products of Grassmanians. We constructExpand