Related papers: Equivariant Schubert calculus and geometric Satake

The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the monotone secant conjecture is a compelling generalization of…

In this note we describe the cohomology ring of the Grassmannian of $k$-planes in $n$-dimensional complex vector space as an $\mathrm{GL}_n$-module. We give explicit formulas for the operators of its principal $\mathfrak{sl}_2$-triple. It…

The goal of the paper is to introduce a version of Schubert calculus for each dihedral reflection group W. That is, to each "sufficiently rich'' spherical building Y of type W we associate a certain cohomology theory and verify that, first,…

We show that sigma models with orthogonal and symplectic Grassmannian target spaces admit chiral Gross-Neveu model formulations, thus extending earlier results on unitary Grassmannians. As a first application, we calculate the one-loop…

Boij-S\"oderberg theory characterizes syzygies of graded modules and sheaves on projective space. This paper continues earlier work with S. Sam, extending the theory to the setting of $GL_k$-equivariant modules and sheaves on Grassmannians.…

A solution is given to the following problem: how to compute the multiplicity, or more generally the Hilbert function, at a point on a Schubert variety in an orthogonal Grassmannian. Standard monomial theory is applied to translate the…

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear…

We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant K-theory algebra of the cotangent bundle. This description is based on the hypergeometric…

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…

We use a theorem of Tolman and Weitsman to find explicit formul\ae for the rational cohomology rings of the symplectic reduction of flag varieties in C^n, or generic coadjoint orbits of SU(n), by (maximal) torus actions. We also calculate…

Let $LG_n$ denote the Lagrangian Grassmannian parametrizing maximal isotropic (Lagrangian) subspaces of a fixed symplectic vector space of dimension $2n.$ For each strict partition $\lambda=(\lambda_1,...,\lambda_k)$ with $\lambda_1\leq n$…

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…

This is an expanded version of the text ``Perverse Sheaves on Loop Grassmannians and Langlands Duality'', AG/9703010. The main new result is a topological realization of algebraic representations of reductive groups over arbitrary rings. We…

We prove that the dimension of the Specht module of a forest $G$ is the same as the normalized volume of the matching polytope of $G$. We also associate to $G$ a symmetric function $s_G$ (analogous to the Schur symmetric function…

The potential that generates the cohomology ring of the Grassmannian is given in terms of the elementary symmetric functions using the Waring formula that computes the power sum of roots of an algebraic equation in terms of its…

Let $G/P$ be a complex cominuscule flag manifold. We prove a type independent formula for the torus equivariant Mather class of a Schubert variety in $G/P$, and for a Schubert variety pulled back via the natural projection $G/Q \to G/P$. We…

We examine the relationship between the (double) Schubert polynomials of Billey-Haiman and Ikeda-Mihalcea-Naruse and the (double) theta and eta polynomials of Buch-Kresch-Tamvakis and Wilson from the perspective of Weyl group invariants. We…

We introduce a family of tableaux that simultaneously generalizes the tableaux used to characterize Grothendieck polynomials and k-Schur functions. We prove that the polynomials drawn from these tableaux are the affine Grothendieck…

Ehrhart polynomials are extensively-studied structures that interpolate the discrete volume of the dilations of integral $n$-polytopes. The coefficients of Ehrhart polynomials, however, are still not fully understood, and it is not known…

We study the algebra of Wilson line operators in three-dimensional N=2 supersymmetric U(M) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M,N), and its connection to K-theoretic Gromov-Witten invariants for Gr(M,N).…