Related papers: Jacquet functor and De Concini-Procesi compactific…
We describe the Jacquet module functor on Harish-Chandra modules via geometry.
We give an action of $N$ on the geometric Jacquet functor defined by Emerton-Nadler-Vilonen.
The aim of this article is to study the functorial properties of the ``formal geometric quantization'' procedure which is defined for non-compact Hamiltonian manifolds (when the moment map is proper). For this purpose, we introduce a…
We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the…
In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results…
Associated to any subspace arrangement is a "De Concini-Procesi model", a certain smooth compactification of its complement, which in the case of the braid arrangement produces the Deligne-Mumford compactification of the moduli space of…
We introduce a deformation of Cayley's second hyperdeterminant for even-dimensional hypermatrices. As an application, we formulate a generalization of the Jacobi-Trudi formula for Macdonald functions of rectangular shapes generalizing…
Wonderful compactifications of adjoint reductive groups over an algebraically closed field play an important role in algebraic geometry and representation theory. In this paper, we construct an equivariant compactification for adjoint…
We calculate the $k$-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for $k=1$ to derive a closed-form expression for eigenvalue density. For real matrices we…
This expository article outlines the construction of De Concini-Procesi arrangement models and describes recent progress in understanding their significance from the algebraic, geometric, and combinatorial point of view. Throughout the…
We look at the decomposition of the compactified jacobian of a singular curve into components and discuss some examples.
Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.
Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.
We give an iterative method to realize general Jack functions from Jack functions of rectangular shapes. We first show some cases of Stanley's conjecture on positivity of the Littlewood-Richardson coefficients, and then use this method to…
In this paper, we present a unified approach using model category theory and an associative law to compare some classic variants of the geometric realization functor.
In this paper we study a generalization of the Jacquet module of a parabolic induction and construct a filtration on it. The successive quotient of the filtration is written by using the twisting functor.
Jacobi's elliptic functions have been constructed from a deformed Lie algebra. The generators of the algebra have been obtained from a bi-orthogonal system. The deformation parameter resembles the modulus of the relevant elliptic functions.
In this thesis, we study the Casselman-Jacquet functor. We discuss a new technical approach which makes the Casselman-Jacquet functor right adjoint to the Bernstein functor. We give an explanation, using D-modules, of the Bruhat filtration…
We construct and analyze the Jacobi process - in mathematical biology referred to as Wright-Fisher diffusion - using a Dirichlet form. The corresponding Dirichlet space takes the form of a Sobolev space with different weights for the…
This article gives a natural decomposition of the suspension of generalized moment-angle complexes or {\it partial product spaces} which arise as {\it polyhedral product functors} described below. In the special case of the complements of…