相关论文: A geometric Jacquet functor
We give an action of $N$ on the geometric Jacquet functor defined by Emerton-Nadler-Vilonen.
We give a geometric realization of the Jacquet functor using a deformation of De Concini-Procesi compactification.
Kei Yuen Chan and Kayue Daniel Wong constructed a functor from the category of Harish-Chandra modules of $\mathrm{GL}(n, \mathbb C)$ to the category of modules over graded Hecke algebra $\mathbb H_m$ of type A. This functor has several nice…
We define an affine Jacquet functor and use it to describe the structure of induced affine Harish-Chandra modules at noncritical levels, extending the theorem of Kac and Kazhdan [KK] on the structure of Verma modules in the…
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.
Let (G,K) be a symmetric pair over the complex numbers, and let X=K\G be the corresponding symmetric space. In this paper we study a nearby cycles functor associated to a degeneration of X to MN\G, which we call the "wonderful…
We propose a new approach for the study of the Jacquet module of a Harish-Chandra module of a real semisimple Lie group. Using this method, we investigate the structure of the Jacquet module of principal series representation generated by…
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…
Reflexive functors of modules naturally appear in Algebraic Geometry. In this paper we define a wide and elementary family of reflexive functors of modules, closed by tensor products and homomorphisms, in which Algebraic Geometry can be…
In this note we discuss the concept of Harish-Chandra modules over the integers. The main result is a rationality result for certain intertwining operator which is used in a joint paper with Raghuram. We also discuss an interesting question…
We classify Harish-Chandra bimodules over the quantized flower quiver varieties with minimal support. We show that if the dimension vector is $n$, then there are $n!$ minimally supported simple Harish-Chandra bimodules for integral…
We construct the reflection functors for quiver Hecke algebras of an arbitrary symmetrizable Kac-Moody type. These reflection functors categorify Lusztig's braid symmetries.
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
A way to add an extra dimension is briefly discussed.
Let F be a finite field and G=GL(6,F). In this paper, we explicitly describe a certain twisted Jacquet module of an irreducible cuspidal representation of G.
We continue the study of the fundamental series of generalized Harish-Chandra modules initiated in [PZ2]. Generalized Harish-Chandra modules are (g,k)-modules of finite type where g is a semisimple Lie algebra and k \subset g is a reductive…
We provide some examples of harmonic unit vector fields as normalized gradients of isoparametric functions from a K-contact geometry setting.
We construct twisting functors for quantum group modules. First over the field $\mathbb{Q}(v)$ but later over any $\mathbb{Z} [v,v^{-1}]$-algebra. The main results in this paper are a rigerous definition of these functors, a proof that they…
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many…
In this paper, we classify simple Harish-Chandra modules over simple generalized Witt algebras.