Abstract
AbstractThis paper gives a classification of stable vectors in dual Vinberg representations coming from a graded Lie algebra of type F4 in a way that is independent of the field of definition. Relating these gradings to Moy–Prasad filtrations, we obtain the input for Reeder–Yu’s construction of epipelagic supercuspidal representations. As a corollary, this construction gives new supercuspidal representations of $F_{4}(\mathbb {Q}_{p})$
F
4
(
ℚ
p
)
when p is small.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
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