Related papers: The Langlands-Weissman Program for Brylinski-Delig…
We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. We work with all covers that arise from extensions of quasisplit reductive groups by $\mathbf{K}_2$ -- the…
Let T be a split torus over local or global function field. The theory of Brylinski-Deligne gives rise to the metaplectic central extensions of T by a finite cyclic group. The representation theory of these metaplectic tori has been…
We determine the finite group $\mathcal S$ parametrizing a packet in the local Langlands correspondence for a Brylinski-Deligne covering group of an algebraic torus, under some assumption on ramification. Especially, this work generalizes…
We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex…
In this joint introduction to an Asterisque volume, we give a short discussion of the historical developments in the study of nonlinear covering groups, touching on their structure theory, representation theory and the theory of automorphic…
Kottwitz suggested to study all extended pure inner forms together in the local Langlands correspondence for linear reductive groups. We extend this philosophy to a large class of covers, including those defined by Brylinski and Deligne,…
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…
We adapt the conjectural local Langlands parameterization to split metaplectic groups over local fields. When $\tilde G$ is a central extension of a split connected reductive group over a local field (arising from the framework of Brylinski…
Langlands has described the irreducible admissible representations of $T$, when $T$ is the group of points of an algebraic torus over a local field. Also, Langlands described the automorphic representations of $T_{\mathbb A}$ when…
A global packet may simultaneously contain an automorphic representation and a non-automorphic representation. The global $\mathcal S$-group is expected, and known in some cases, to specify the automorphic representations in each global…
For finite topological central extensions of $p$-adic classical groups, Heiermann and Wu introduced the notion of decomposed Levi subgroups in their study of intertwining algebras. In this note, we show that for symplectic and special…
The theory of intertwining operators plays an important role in the development of the Langlands program. This, in some sense, is a very sophisticated theory, but the basic question of its singularity, in general, is quite unknown.…
We study the dimension of the space of Whittaker functionals for depth zero representations of covering groups. In particular, we determine such dimensions for arbitrary Brylinski-Deligne coverings of the general linear group. The results…
In this paper we study a notion of HL-extension (HL standing for Herwig--Lascar) for a structure in a finite relational language $\mathcal{L}$. We give a description of all finite minimal HL-extensions of a given finite…
A brief survey is given of the classical Langlands correspondence between n-dimensional representations of Galois groups of local and global fields of dimension 1 and irreducible representations of the groups GL(n). A generalization of the…
For Brylinski-Deligne covering groups of an arbitrary split reductive group, we consider theta representations attached to certain exceptional genuine characters. The goal of the paper is to determine when a theta representation has exactly…
Let $K$ be a local non-Archimedean field of positive characteristic and let $L$ be the degree-$n$ unramified extension of $K$. Via the local Langlands and Jacquet-Langlands correspondences, to each sufficiently generic multiplicative…
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.
We explain how to develop the twisted doubling integrals for Brylinski-Deligne extensions of connected classical groups. This gives a family of global integrals which represent Euler products for this class of non-linear extensions.
Inspired by Ol'shanskii's work, we provide an axiomatic framework to describe certain irreducible unitary representations of non-discrete unimodular totally disconnected locally compact groups. We then look at the applications to certain…