Related papers: Schubert defects in Lagrangian Grassmannians

Several moduli spaces parametrizing linear subspaces of the projective space are cut out by linear and quadratic equations in their natural embedding: Grassmannians, Flag varieties, and Schubert varieties. The goal of this paper is to prove…

We consider the problem of determining Gr\"obner bases of binomial ideals associated with linear error correcting codes. Computation of Gr\"obner bases of linear codes have become a topic of interest to many researchers in coding theory…

In this tutorial, we provide an overview of many of the established combinatorial and algebraic tools of Schubert calculus, the modern area of enumerative geometry that encapsulates a wide variety of topics involving intersections of linear…

We give formulas for the products of classes of Schubert varieties in the quantum cohomology rings of Grassmannians, in terms of the combinatorics of partitions and tableaux.

This paper studies, for a positive integer $m$, the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most $m$. We build in two ways upon a conjecture for the Hilbert series of this…

A. Mironov proposed a construction of lagrangian submanifolds in $\mathbb{C}^n$ and $\mathbb{C} \mathbb{P}^n$; there he was mostly motivated by the fact that these lagrangian submanifolds (which can have in general self intersections,…

We exhibit quantum cluster algebra structures on quantum Grassmannians $K_q[Gr(2,n)]$ and their quantum Schubert cells, as well as on $K_q[Gr(3,6)]$, $K_q[Gr(3,7)]$ and $K_q[Gr(3,8)]$. These cases are precisely those where the quantum…

This article presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials for shapes that are naturally embedded in a torus. Then we…

We construct defects describing the transition between different phases of gauged linear sigma models with higher rank abelian gauge groups, as well as defects embedding these phases into the GLSMs. Our construction refers entirely to the…

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher rank field-strength tensors. The integrals of these forms over the corresponding space-time coordinates provides new…

The symmetric Grothendieck polynomials representing Schubert classes in the $K$-theory of Grassmannians are generating functions for semistandard set-valued tableaux. We construct a type $A_n$ crystal structure on these tableaux. This…

In this paper we explore nonabelian gauged linear sigma models (GLSMs) for symplectic and orthogonal Grassmannians and flag manifolds, checking e.g. global symmetries, Witten indices, and Calabi-Yau conditions, following up a proposal in…

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and…

Let $L_w$ be the Levi part of the stabilizer $Q_w$ in $GL_N$ (for left multiplication) of a Schubert variety $X(w)$ in the Grassmannian $G_{d,N}$. For the natural action of $L_w$ on $\mathbb{C}[X(w)]$, the homogeneous coordinate ring of…

We show that general isotropic flags for odd-orthogonal and symplectic groups are general for Schubert calculus on the classical Grassmannian in that Schubert cells defined by such flags meet transversally. This strengthens a result of…

Polynomial solutions to the KP hierarchy are known to be parametrized by a cone over an infinite-dimensional Grassmann variety. Using the notion of Schubert derivation on a Grassmann algebra, we encode the classical Pl\"ucker equations of…

The variety of consistent "gauging" deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions.…

We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also…

The relationship of two dimensional quantum field theory and isomonodromic deformations of Fuchsian systems has a long history. Recently four-dimensional $\mathcal{N}=2$ gauge theories joined the party in a multitude of roles. In this paper…

We study the evolution of matter density perturbations in Galileon cosmology where the late-time cosmic acceleration can be realized by a field kinetic energy. We obtain full perturbation equations at linear order in the presence of five…