arXiv math/99122081999-12math.AGmath.NTmath.RT

Gamma-functions of representations and lifting

Alexander Braverman, David Kazhdan, V. Vologodsky

备注：: Main text by Alexander Braverman and David Kazhdan with an appendix by V. Vologodsky. Several minor mistakes corrected

英文摘要：

Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual group of F one can associate certain meromorphic function on the set of isomorphism classed of irreducible representations of G (which we call gamma-functions). In this paper we describe a general framework for an explicit construction of these gamma-functions. We make this idea precise in certain special cases. As a byproduct we give explicit conjectural formulas for the representation $l_E(θ)$ of the group GL(n,F) associated to a character $θ$ of the multiplicative group $E^*$ of a separable extension E of F of degree n. We also describe a conjectural analogue of the Poisson summation formula associated to a representation of the Langlands dual group, which implies the existence of the meromorphic continuation and functional equation for the corresponding automorphic L-functions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

On the lifting problem of representations of a metacyclic group

We give a necessary and sufficient condition for a modular representation of a group $G=C_{p^h} \rtimes C_m$ in a field of characteristic zero to be lifted to a representation over local principal ideal domain of characteristic zero containing the $p^h$ roots of unity.

2023-01-03math.AGmath.RT

通过 Galois 上同调提升 Galois 表示

Lifting Galois representations via Galois cohomology

本文综述了通过 Galois 上同调提升 Galois 表示的近期进展，重点介绍了仅依赖 Galois 上同调的方法及 Ottawa 会议相关内容。

2025-08-13math.AGmath.NT

Projective representations of fundamental groups of quasiprojective varieties: a realization and a lifting result

We discuss two results about projective representations of fundamental groups of quasiprojective varieties. The first is a realization result which, under a nonresonance assumption, allows to realize such representations as monodromy representations of flat projective logarithmic connections. The second is a lifting result: any representation as above, after restriction to a Zariski open set and finite pull-back, can be lifted to a linear representation.

2014-11-12math.AGmath.CV

当 $\u2113 \u2260 p$ 时提升 $G$ 值伽罗瓦表示

Lifting $G$-Valued Galois Representations when $\ell \neq p$

本文研究ℓ≠p时任意约化群概形值局部伽罗瓦表示的通用提升空间，构造典范光滑分支推广极小分歧形变条件，引入弱约化群概形解决概形论问题，可用于整体伽罗瓦表示的几何提升。

2024-10-07math.AGmath.NT

Lifting mappings over invariants of finite groups

We characterize those regular, holomorphic or formal maps into the orbit space $V/G$ of a complex representation of a finite group $G$ which admit a regular, holomorphic or formal lift to the representation space $V$. In particular, the case of complex reflection groups is investigated.

2003-12-01math.AGmath.RT

Lifting systems of Galois representations associated to abelian varieties

This paper treats what we call `weak geometric liftings' of Galois representations associated to abelian varieties. This notion can be seen as a generalization of the idea of lifting a Galois representation along an isogeny of algebraic groups. The weaker notion only takes into account an isogeny of the derived groups and disregards the centres of the groups in question. The weakly lifted representations are required to be geometric in the sense of a conjecture of Fontaine and Mazur. The conjecture in question states that any irreducible geometric representation is a twist of a subquotient of …

2006-12-30math.AGmath.NT

更多相关论文收起更多论文

Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case

We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We use these results to prove many new cases of the strong Artin conjecture over totally real fields in which 5 is unramified. As an ingredient of the proof, we provide a general result on the automatic analytic continuation of overconvergent p-adic Hilbert modular forms of finite slope which substantially generalizes a similar result in arXiv:1111.2804.

2013-05-21math.AGmath.NT

Partition function of beta-gamma system on orbifolds

Partition function of beta-gamma systems on the orbifolds C^2/Z_N and C^3/Z_M x Z_N are obtained as the invariant part of that on the respective affine spaces, by lifting the geometric action of the orbifold group to the fields. Interpreting the sum over roots of unity as an elementary contour integration, the partition function evaluates to an infinite series counting invariant monomials composed of basic operators of the theory at each mass level.

2013-11-24hep-thmath.AGmath.RT

关于Braverman和Kazhdan的一个猜想

On a conjecture of Braverman and Kazhdan

本文针对GL(n)证明了Braverman和Kazhdan关于特定仿射空间上l-adic γ层无圈性的猜想9.12，解决了表示论与层论交叉领域的一个关键问题。

2016-02-18math.AGmath.RT

A generalization of Puiseux's theorem and lifting curves over invariants

Let $ρ: G \to \operatorname{GL}(V)$ be a rational representation of a reductive linear algebraic group $G$ defined over $\mathbb C$ on a finite dimensional complex vector space $V$. We show that, for any generic smooth (resp. $C^M$) curve $c : \mathbb R \to V // G$ in the categorical quotient $V // G$ (viewed as affine variety in some $\mathbb C^n$) and for any $t_0 \in \mathbb R$, there exists a positive integer $N$ such that $t \mapsto c(t_0 \pm (t-t_0)^N)$ allows a smooth (resp. $mathbb C^M$) lift to the representation space near $t_0$. ($C^M$ denotes the Denjoy--Carleman class associated w…

2011-01-31math.AGmath.RT

Refined Swan conductors mod p of one-dimensional Galois representations

For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.

2018-09-05math.AGmath.NT

Families of p-adic Galois representations and (phi,Gamma)-modules

We investigate the relation between p-adic Galois representations and overconvergent (phi,Gamma)-modules in families. Especially we construct a natural open subspace of a family of (phi,Gamma)-modules, over which it is induced by a family of Galois-representations.

2012-02-15math.AGmath.NT

Lifting quasianalytic mappings over invariants

Let $ρ: G \to \operatorname{GL}(V)$ be a rational finite dimensional complex representation of a reductive linear algebraic group $G$, and let $σ_1,σ_n$ be a system of generators of the algebra of invariant polynomials $\mathbb{C}[V]^G$. We study the problem of lifting mappings $f : \mathbb{R}^q \supseteq U \to σ(V) \subseteq \mathbb{C}^n$ over the mapping of invariants $σ=(σ_1,σ_n) : V \to σ(V)$. Note that $σ(V)$ can be identified with the categorical quotient $V /\!\!/ G$ and its points correspond bijectively to the closed orbits in $V$. We prove that, if $f$ belongs to a quasianalytic subcl…

2011-01-12math.AGmath.CAmath.RT

Lifting low-dimensional local systems

Let $k$ be a field of characteristic $p>0$. Denote by $W_r(k)$ the ring of truntacted Witt vectors of length $r \geq 2$, built out of $k$. In this text, we consider the following question, depending on a given profinite group $G$. $Q(G)$: Does every (continuous) representation $G\longrightarrow GL_d(k)$ lift to a representation $G\longrightarrow GL_d(W_r(k))$? We work in the class of cyclotomic pairs (Definition 4.3), first introduced in [DCF] under the name "smooth profinite groups". Using Grothendieck-Hilbert' theorem 90, we show that the algebraic fundamental groups of the following schemes…

2021-05-23math.AG