# Principal series representations of metaplectic groups

@article{Tang2017PrincipalSR, title={Principal series representations of metaplectic groups}, author={Shiang Tang}, journal={arXiv: Representation Theory}, year={2017} }

We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order $n$. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.

#### References

SHOWING 1-10 OF 14 REFERENCES

Principal Series Representations of Metaplectic Groups Over Local Fields

- Mathematics
- 2012

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension \(\widetilde{G}\) of G by a cyclic group of order n, under… Expand

Modular forms on non-linear double covers of algebraic groups

- Mathematics
- 2010

We construct automorphic representations of non-linear two-fold covers of simply connected Chevalley groups via residues of Eisenstein series. In the process, we establish some basic results in… Expand

Action of Intertwining operators on pseudospherical K-types

- Mathematics
- 2015

In this paper, we give a concrete description of the two-fold cover of a simply connected, split real reductive group and its maximal compact subgroup as Chevalley groups. We define a representation… Expand

Plancherel measures for coverings of p-adic SL(2,F)

- Mathematics
- 2014

In these notes we compute the Plancherel measures associated with genuine principal series representations of n-fold covers of p-adic SL(2,F). Along the way we also compute a higher dimensional… Expand

Unitary Shimura correspondences for split real groups

- Mathematics
- 2007

We find a relationship between certain complementary series representations for nonlinear coverings of split simple groups, and spherical complementary series for (different) linear groups. The main… Expand

Lectures on Representations of p-adic Groups

- Mathematics
- 2004

This text contains an elementary introduction, with exercises, to representations of p-adic reductive groups. The text is intended to be more accessible then the standard references, such as the… Expand

The Langlands-Weissman Program for Brylinski-Deligne extensions

- Mathematics
- 2014

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… Expand

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

- Mathematics
- 2014

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… Expand

Covers of tori over local and global fields

- Mathematics
- 2014

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… Expand