相关论文: Some results about the geometric Whittaker model

We partially generalize the theory of semihomogeneous bundles on an abelian variety $A$ developed by Mukai. This involves considering abelian subvarieties $Y\subset X_A=A\times\hat{A}$ and studying coherent sheaves on $A$ invariant under…

Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the…

In their proof of the Drinfeld-Langlands correspondence, Frenkel, Gaitsgory and Vilonen make use of a geometric Fourier transformation. Therefore, they work either with l-adic sheaves in characteristic p>0, or with D-modules in…

Using a combinatorial approach which avoids geometry, this paper studies the ring structure of K_T(G/B), the T-equivariant K-theory of the (generalized) flag variety G/B. Here the data is a complex reductive algebraic group (or…

We obtain necessary and sufficient conditions for the admissible vectors of a new unitary non irreducible representation $U$. The group $G$ is an arbitrary semidirect product whose normal factor $A$ is abelian and whose homogeneous factor…

Let G be a connected simple linear Lie group and H in G a symmetric subgroup such that the corresponding symmetric space G/H is non-compactly causal. We show that any irreducible unitary representation of G leads naturally to a net of…

Given a Chevalley group $\mathcal{G}$ of classical type and a Borel subgroup $\mathcal{B} \subseteq \mathcal{G}$, we compute the $\Sigma$-invariants of the $S$-arithmetic groups $\mathcal{B}(\mathbb{Z}[1/N])$, where $N$ is a product of…

We show that for a reductive group $G$ over a field $k$ the $\mathbb{A}^1$-Euler characteristic of the variety of maximal tori in $G$ is an invertible element of the Grothendieck-Witt ring $\mathrm{GW}(k)$, settling the weak form of a…

For $G$ an algebraic group definable over a model of $\operatorname{ACVF}$, or more generally a definable subgroup of an algebraic group, we study the stable completion $\widehat{G}$ of $G$, as introduced by Loeser and the second author.…

To generalize some fundamental results on group schemes to the super context, we study the quotient sheaf $G \tilde{/} H$ of an algebraic supergroup $G$ by its closed supersubgroup $H$, in arbitrary characteristic $\neq$ 2. Our main theorem…

We provide a computable criterion for selecting among Fourier, wavelet, and time-frequency analysis by extending the algebraic diversity (AD) framework to Lie groups acting on $L^2(\mathbb{R})$. To our knowledge, there is no other criterion…

We initiate the study of the Stone-\v{C}ech transformation groupoid $\mathcal{G} = \mathcal{S}\ltimes\beta\mathcal{S}$ of an inverse semigroup $\mathcal{S}$. We prove that the properties of being Hausdorff, principal, and effective are all…

Let G be a connected reductive group defined over an algebraically closed ground field of characteristic p, let B be a Borel subgroup of G, and let X be a G-variety. The first named author has shown that for p = 0 there is a natural action…

On an abelian variety $A$, sheaf convolution gives a Tannakian formalism for perverse sheaves. Let $X$ be an irreducible algebraic variety with generic point $\eta$. Let $K$ be a family of perverse sheaves (more precisely, a relative…

It is known that the notion of a transitive subgroup of a permutation group $P$ extends naturally to the subsets of $P$. We study transitive subsets of the wreath product $G \wr S_n$, where $G$ is a finite abelian group. This includes the…

We prove an analog of the Gauss-Bonnet formula for constructible sheaves on reductive groups. As a corollary from this formula we get that if a perverse sheaf on a reductive group is equivariant under the adjoint action, then its Euler…

Fix a scheme $X$ over a field of characteristic zero that is equipped with an action of a reductive algebraic group $G$. We give necessary and sufficient conditions for a $G$-equivariant coherent sheaf on $X$ or a bounded-above complex of…

Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…

Let K be a CM-field, i.e., a totally complex quadratic extension of a totally real field F. Let X be a g-dimensional abelian variety admitting an algebra embedding of F into the rational endomorphisms End_Q(X) of X. Let A be the product of…

Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space…