Twisted doubling integrals for Brylinski-Deligne extensions of classical groups

Unramified Whittaker functions for certain Brylinski-Deligne covering groups

For a Brylinski-Deligne covering group of a general linear group, we calculate some values of unramified Whittaker functions for certain representations that are analogous to the theta representations.

The Langlands-Weissman Program for Brylinski-Deligne extensions

We describe an evolving and conjectural extension of the Langlands program for a class of nonlinear covering groups of algebraic origin studied by Brylinski-Deligne. In particular, we describe the construction of an L-group extension of such a covering group (over a split reductive group) due to Weissman, study some of its properties and discuss a variant of it. Using this L-group extension, we describe a local Langlands correspondence for covering (split) tori and unramified genuine representations, using work of Savin, McNamara, Weissman and W.W. Li. Finally, we define the notion of automorp…

The Gindikin-Karpelevich Formula and Constant Terms of Eisenstein Series for Brylinski-Deligne Extensions

We firstly discuss properties of the L-group for Brylinski-Deligne (BD) extensions constructed by M. Weissman. Secondly, the Gindikin-Karpelevich (GK) formula for arbitrary BD extensions is computed and expressed in terms of naturally defined elements of the group. We show that the GK formula can be interpreted as Langlands-Shahidi type L-functions associated with the ajoint action of the L-group of the Levi on certain Lie algebras. As a consequence, the constant term of Eisenstein series for BD extensions could be expressed in terms of global (partial) Langlands-Shahidi type L-functions. In t…

Managing Metaplectiphobia: Covering p-adic groups

Brylinski and Deligne have provided a framework to study central extensions of reductive groups by K2 over a field F. Such central extensions can be used to construct central extensions of p-adic groups by finite cyclic groups, including the metaplectic groups. Particularly interesting is the observation of Brylinski and Deligne that a central extension of a reductive group by K2, over a p-adic field, yields a family of central extensions of reductive groups by the multiplicative group over the residue field, indexed by the points of the building. These algebraic groups over the residue field …

关于某些深度零表示的经典倍增方法伽马因子

On classical doubling method gamma factors for certain depth zero representations

本文研究了经典有限李型群不可约表示的倍增方法伽马因子，证明其乘法性，并通过Deligne-Lusztig数据给出非共轭对偶特征情况下的显式公式，同时将构造与Lapid-Rallis的局部构造联系起来。

关于经典加倍法产生的雅可比和

On Jacobi sums arising from the classical doubling method

研究有限域上一般线性群或经典群相关的非阿贝尔雅可比和，对一般线性群用近藤非阿贝尔高斯和表示，对经典群及特定特征给出显式公式并证明其在几何卢茨蒂格系列上为常数，结果依赖于吉尔施 - 泽林格的乘法性结果。