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Maximality of hyperspecial compact subgroups avoiding Bruhat–Tits theory
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Let
k
be a complete non-archimedean field (non trivially valued). Given a reductive
k
-group
G
, we prove that hyperspecial subgroups of
G
(
k
)
(i.e. those arising from reductive models of
G
) are maximal among bounded subgroups. The originality resides in the argument: it is inspired by the case of
GL
n
and avoids all considerations on the Bruhat–Tits building of
G
.
Title: Maximality of hyperspecial compact subgroups avoiding Bruhat–Tits theory
Description:
Let
k
be a complete non-archimedean field (non trivially valued).
Given a reductive
k
-group
G
, we prove that hyperspecial subgroups of
G
(
k
)
(i.
e.
those arising from reductive models of
G
) are maximal among bounded subgroups.
The originality resides in the argument: it is inspired by the case of
GL
n
and avoids all considerations on the Bruhat–Tits building of
G
.
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