Split metaplectic groups and their L-groups

Details Split metaplectic groups and their L-groups Split metaplectic groups and their L-groups

2011-08-05

arxiv.org/abs/1108.1413v1

Mathematics

Representation Theory

48 pages

Scientific paper

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 and Deligne), we construct a dual group $\mathbf{\tilde G}^\vee$ and an L-group ${}^L \mathbf{\tilde G}^\vee$ as group schemes over ${\mathbb Z}$. Such a construction leads to a definition of Weil-Deligne parameters (Langlands parameters) with values in this L-group, and to a conjectural parameterization of the irreducible genuine representations of $\tilde G$. This conjectural parameterization is compatible with what is known about metaplectic tori, Iwahori-Hecke algebra isomorphisms between metaplectic and linear groups, and classical theta correspondences between $Mp_{2n}$ and special orthogonal groups.

Affiliated with

Also associated with

No associations

Rating

Split metaplectic groups and their L-groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Split metaplectic groups and their L-groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Split metaplectic groups and their L-groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-913