Martin H. Weissman
Split metaplectic groups and their L-groups.
Tue, 08/09/2011 - 15:01 — SomNambulAuthors: Martin H. Weissman
Subjects: Representation Theory
AbstractWe 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
${\mathbb Z}$.Managing Metaplectiphobia: Covering p-adic groups.
Wed, 08/04/2010 - 15:01 — SomNambulAuthors: Martin H. Weissman
Subjects: Number Theory
AbstractBrylinski 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.Dichotomy for generic supercuspidal representations of $G_2$.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Gordan Savin, Martin H. Weissman
Subjects: Representation Theory
AbstractThe local Langlands conjectures imply that to every generic supercuspidal
irreducible representation of $G_2$ over a $p$-adic field, one can associate a
generic supercuspidal irreducible representation of either $PGSp_6$ or$PGL_3$.
We prove this conjectural dichotomy, demonstrating a precise correspondence
between certain representations of $G_2$ and other representations of $PGSp_6$
and $PGL_3$ when $p \neq 2$. This correspondence arises from theta
correspondences in $E_6$ and $E_7$, analysis of Shalika functionals, and spin
L-functions.
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