相关论文: Shalika germs for sl(n) and sp(2n) are motivic

Let $\Pi$ be a cohomological cuspidal automorphic representation of ${\rm GL}_{2n}(\mathbb A)$ over a totally real number field $F$. Suppose that $\Pi$ has a Shalika model. We define a rational structure on the Shalika model of $\Pi_f$.…

Degenerating the action of the elliptic Hall algebra on the Fock space, we give a combinatorial formula for the Shalika germs of tamely ramified regular semisimple elements $\gamma$ of $GL_n$ over a nonarchimedean local field. As a…

Let $F$ be a local field of characteristic $p$ and $G$ be a connected reductive group over $F$. Recall that Shalika's germ expansion of orbital integrals of regular semi-simple elements near the identity, when it exists, is a sum indexed by…

In this article, for nilpotent orbits of ramified quasi-split unitary groups with two Jordan blocks, we give closed formulas for their Shalika germs at certain equi-valued elements with half-integral depth previously studied by Hales. These…

This article has two parallel perspectives: to demonstrate an inductive structure of Shalika germs, and to show an analogous inductive structure for affine Springer fibers. More precisely, we give an algorithm to compute arbitrary Shalika…

Let F be either R or C. Let $(\pi,V)$ be an irreducible admissible smooth \Fre representation of GL(2n,F). A Shalika functional $\phi:V \to \C$ is a continuous linear functional such that for any $g\in GL_n(F), A \in \Mat_{n \times n}(F)$…

For a reductive group $G$ over a non-archimedean local field, with some assumptions on (residue) characteristic we give an method to compute certain orbital integrals using a method close to that of Goresky-Kottiwitz-MacPherson but in a…

Let k be a field and denote by SH(k) the motivic stable homotopy category. Recall its full subcategory HI_0(k) of effective homotopy modules. Write NAlg(HI_0(k)) for the category of normed motivic spectra with underlying spectrum an…

This article constructs Shalika germs in the context of motivic integration, both for ordinary orbital integrals and kappa-orbital integrals. Based on transfer principles in motivic integration and on Waldspurger's endoscopic transfer of…

This article gives a proof of the Langlands-Shelstad fundamental lemma for the spherical Hecke algebra for every unramified p-adic reductive group G in large positive characteristic. The proof is based on the transfer principle for…

Let $\mathfrak{Var}_k^G$ denote the category of pairs $(X,\sigma)$, where $X$ is a variety over $k$ and $\sigma$ is a group action on $X$. We define the Grothendieck ring for varieties with group actions as the free abelian group of…

In this paper, we prove that a $\mathrm{GL}(2n)$-eigenvariety is \'etale over the (pure) weight space at non-critical Shalika points, and construct multi-variable $p$-adic $L$-functions varying over the resulting Shalika components. Our…

Let $\Gamma$ be the fundamental group of a manifold modeled on three dimensional Sol geometry. We prove that $\Gamma$ has a finite index subgroup $G$ which has a rational growth series with respect to a natural generating set. We do this by…

We investigate several interrelated foundational questions pertaining to the study of motivic dga's of Dan-Cohen--Schlank [8] and Iwanari [13]. In particular, we note that morphisms of motivic dga's can reasonably be thought of as a…

We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth representations of GL(n,F) where F is a finite extension of Q_p and l is different from p. To do so, we also extend the theory of Rankin-Selberg integrals, first…

Let $\Sigma$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $\Sigma$ over the field of rational functions can be algebraically generated by a finite…

Let $\gg$ be a complex reductive Lie algebra and $\kk\subset\gg$ be any reductive in $\gg$ subalgebra. We call a $(\gg,\kk)$-module $M$ bounded if the $\kk$-multiplicities of $M$ are uniformly bounded. In this paper we initiate a general…

In this paper a quantum analog of the $*$-algebra of regular functions on the Shilov boundary $S(\mathbb D)$ of bounded symmetric domain $\mathbb D$ is constructed. The algebras of regular functions on $S(\mathbb D)$ are described in terms…

Whittaker functions of $GL(n, \mathbb R)$ , are most known for its role in the Fourier-Whittaker expansion of cusp forms. Their behavior in the Siegel set, in large, is well-understood. In this paper, we insert into the literature some…

The authors establish the fundamental lemma for a relative trace formula. This trace formula compares generic automorphic representations of GSp$(4)$ with automorphic representations of GL$(4)$ which are distinguished with respect to a…