Corpus ID: 45946409

Principal series representations of metaplectic groups

@article{Tang2017PrincipalSR,
  title={Principal series representations of metaplectic groups},
  author={Shiang Tang},
  journal={arXiv: Representation Theory},
  year={2017}
}
  • Shiang Tang
  • Published 2017
  • Mathematics
  • arXiv: Representation Theory
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
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, underExpand
Modular forms on non-linear double covers of algebraic groups
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 inExpand
Action of Intertwining operators on pseudospherical K-types
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 representationExpand
Plancherel measures for coverings of p-adic SL(2,F)
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 dimensionalExpand
Unitary Shimura correspondences for split real groups
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 mainExpand
Lectures on Representations of p-adic Groups
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 theExpand
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 theExpand
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 computedExpand
Covers of tori over local and global fields
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 automorphicExpand
...
1
2
...