Related papers: Cyclic Demazure modules and positroid varieties

We provide a proof that every Schubert variety of a semi-infinite flag variety is projectively normal. This gives us an interpretation of a Demazure module of a global Weyl module of a current Lie algebra as the (dual) space of the space of…

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…

In [7], a notion of constant scalar curvature metrics on piecewise flat manifolds is defined. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we define a class of vertex transitive metrics on certain…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise…

We define Chern-Schwartz-MacPherson (CSM) cycles of an arbitrary matroid. These are balanced weighted fans supported on the skeleta of the corresponding Bergman fan. In the case that the matroid arises from a complex hyperplane arrangement…

The_commuting variety_ is the pairs of NxN matrices (X,Y) such that XY = YX. We introduce the_diagonal commutator scheme_, {(X,Y) : XY-YX is diagonal}, which we prove to be a reduced complete intersection, one component of which is the…

The discrete polymatroid is a multiset analogue of the matroid. Based on the polyhedral theory on integral polymatroids developed in late 1960's and in early 1970's, in the present paper the combinatorics and algebra on discrete…

In this paper we introduce toric rings of multicomplexes. We show how to compute the divisor class group and the class of the canonical module when the toric ring is normal. In the special case that the multicomplex is a discrete…

We define a convex-polynomial to be one that is a convex combination of the monomials $\{1, z, z^2, \ldots\}$. This paper explores the intimate connection between peaking convex-polynomials, interpolating convex-polynomials, invariant…

In this paper we review and study $R$-modules $M$ for which $S = End_R(M)$ is commutative. For this, we define the concept of center of modules which is a natural generalization of the center of rings. The properties of center of modules,…

Demazure crystals give a combinatorial framework in which to study Demazure modules. They are extremal, in that they satisfy Kashiwara's string property, and they are Demazure atom-positive, in that they decompose naturally into subsets…

We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category…

A positroid is an ordered matroid realizable by a real matrix with all nonnegative maximal minors. Postnikov gave a map from ordered matroids to Grassmann necklaces, for which there is a unique positroid in each fiber of the map. Here, we…

The Hochschild and (cotriple) cyclic homologies of crossed modules of (not-necessarily-unital) associative algebras are investigated. Wodzicki's excision theorem is extended for inclusion crossed modules in the category of crossed modules…

We will construct solvable lattice models whose partition functions are Demazure characters. We will construct a crystal structure on the states of the model and prove that the states of the closed model form a Demazure crystal.

In recent years PBW degenerations of Demazure modules and Schubert varieties were defined and studied in several papers. Various interesting properties (such as these PBW degenerations embedding naturally into the corresponding degenerate…

We provide a characterisation of when a single-element contraction of a transversal matroid is itself transversal. Using this characterisation, we define a new class of transversal matroids closed under minors, which we call path-circular…

Given an abelian variety $A$ defined over a finite field $k$, we say that $A$ is "cyclic" if its group $A(k)$ of rational points is cyclic. In this paper we give a bijection between cyclic abelian varieties of an ordinary isogeny class…

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative…