Related papers: Elliptic classes of Schubert varieties via Bott-Sa…

This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t_1, t_2,...,t_n]. We show these group actions are the same as an action of simple…

The standard Poisson structures on the flag varieties G/P of a complex reductive algebraic group G are investigated. It is shown that the orbits of symplectic leaves in G/P under a fixed maximal torus of G are smooth irreducible locally…

We consider the symplectic groupoid of pairs $(B,\mathbb{A})$ with $\mathbb A$ unipotent upper-triangular matrices and $B\in GL_n$ being such that $\widetilde {\mathbb A}=B{\mathbb A} B^{\text{T}}$ are also unipotent upper-triangular…

For $G$ a finite group acting linearly on $\mathbb{A}^2$, the equivariant Hilbert scheme $\operatorname{Hilb}^r[\mathbb{A}^2/G]$ is a natural resolution of singularities of $\operatorname{Sym}^r(\mathbb{A}^2/G)$. In this paper we study the…

Let $\mathbb{G}$ be a split connected reductive group scheme over the ring of integers $\mathfrak{o}$ of a finite extension $L|\mathbb{Q}_p$ and $\lambda\in X(\mathbb{T})$ an algebraic character of a split maximal torus…

Let $X\subseteq G\slash B$ be a Schubert variety in a flag manifold and let $\pi: \tilde X \rightarrow X$ be a Bott-Samelson resolution of $X$. In this paper we prove an effective version of the decomposition theorem for the derived…

In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular…

Let G be a simply-connected simple compact Lie group over the complex numbers. The affine Grassmannian is a projective ind-variety, homotopy-equivalent to the loop space of G and closely analogous to a maximal flag variety of the classical…

We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron…

We construct an algebra morphism from the elliptic quantum group $E_{\tau,\eta}(sl_2)$ to a certain elliptic version of the ``quantum groups in higher genus'' studied by V. Rubtsov and the first author. This provides an embedding of…

We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is assumed that the weights belong to the Muckenhoupt class $A_p$…

We prove that irreducible representations of the elliptic affine Hecke algebras of Ginzburg, Kapranov, and Vasserot are in one-to-one correspondence with certain nilpotent Higgs bundles on the elliptic curve. The main tool we use is the…

Let A be an abelian variety over a number field K. An identity between the L-functions L(A/K_i,s) for extensions K_i of K induces a conjectural relation between the Birch-Swinnerton-Dyer quotients. We prove these relations modulo finiteness…

Let R be the polynomial ring in n variables, acted on by the symmetric group S_n. Soergel constructed a full monoidal subcategory of R-bimodules which categorifies the Hecke algebra, whose objects are now known as Soergel bimodules. Soergel…

We describe a direct connection between the representation theory of the general linear group and classical Schubert calculus on the Grassmannian, which goes via the Chern-Weil theory of characteristic classes. We also explain why the…

We study properties of the Hirzebruch class of quotient singularities $\mathbb{C}^n/G$, where $G$ is a finite matrix group. The main result states that the Hirzebruch class coincides with the Molien series of $G$ under suitable substitution…

Let $G$ be a Lie group with a maximal torus $T$. Combining Schubert calculus in the flag manifold $G/T$ with the Serre spectral sequence of the fibration $G\rightarrow G/T$, we construct the integral cohomology ring $H^{\ast}(G)$ uniformly…

A flag variety is a homogenous variety $G/B$ where $G$ is a simple algebraic group over the complex numbers and $B$ is a Boel subgroup of $G$. A Schubert variety $X_w$ is a subvariety of $G/B$ indexed by an element $w$ in the Weyl group of…

The aim of this paper is to extend some arithmetic results on elliptic modular forms to the case of Hilbert modular forms. Among these results let's mention : (1) the control of the image of the Galois representation modulo $p$, (2) Hida's…

The variety of complete quadrics is the wonderful compactification of $GL_n/O_n$ and admits a cell decomposition into Borel orbits indexed by combinatorial objects called $\mu$-involutions. We study Coxeter-theoretic properties of…