Related papers: Minimal equations for matrix Schubert varieties

We give a short proof that essentially all questions concerning singularities of Richardson varieties reduce to corresponding questions about Schubert varieties. Consequently, we quickly deduce some new and previously known results.

In this paper we exhibit a minimal set of generators form the annihilator of even neat elements of the exterior algebra of a vector space, when the base field is of positive characteristic and thus we prove the conjecture we established in…

We consider the characterizations of positive definite as well as nonnegative definite quadratic forms in terms of the principal minors of the associated symmetric matrix. We briefly review some of the known proofs, including a classical…

Our main theorems provide a single geometric setting in which polynomial representatives for Schubert classes in the integral cohomology ring of the flag manifold are determined uniquely, and have positive coefficients for geometric…

Using combinatorial properties of symmetric polynomials, we compute explicitly the Soergel modules for some permutations whose corresponding Schubert varieties are rationally smooth. We build from them diagram algebras whose module…

We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.

In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…

We provide the Grobner basis and the primary decomposition of the ideals generated by 2 by 2 permanents of Hankel matrices.

This paper explores the possible use of Schubert cells and Schubert varieties in finite geometry, particularly in regard to the question of whether these objects might be a source of understanding of ovoids or provide new examples. The main…

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary…

We present explicit formulas for a set of generators of the ideal of relations among the pfaffians of the principal minors of the antisymmetric matrices of fixed dimension. These formulas have an interpretation in terms of the standard…

We compute a complete set of non-isomorphic minimal Auslander generators for the exterior algebra in two variables.

We prove Schauder type estimates for solutions of stationary and evolution equations driven by weak generators of transition semigroups associated to a semilinear stochastic partial differential equations with values in a separable Hilbert…

We propose a combinatorial model for the Schubert structure constants of the complete flag manifold when one of the factors is Grassmannian.

We define a version of multiplier ideals, the Mather multiplier ideals, on a variety with arbitrary singularities, using the Mather discrepancy and the Jacobian ideal. In this context we prove a relative vanishing theorem, thus obtaining…

We survey some recent results on the minimal graded free resolution of a square-free monomial ideal. The theme uniting these results is the point-of-view that the generators of a monomial ideal correspond to the maximal faces (the facets)…

It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…

We prove in type A a conjecture which describes the ideal of transversal slices to spherical Schubert varieties in the affine Grassmannian. As a corollary, we prove a modular description (due to Finkelberg-Mirkovi\'c) of the spherical…

We consider partial symmetric Toeplitz matrices where a positive definite completion exists. We characterize those patterns where the maximum determinant completion is itself Toeplitz. We then extend these results with positive definite…

We compute the initial ideals, with respect to certain conveniently chosen term orders, of ideals of tangent cones at torus fixed points to Schubert varieties in orthogonal Grassmannians. The initial ideals turn out to be square-free…