328,674 research outputs found
Conjugacy of Levi subgroups of reductive groups and a generalization to linear algebraic groups
We investigate Levi subgroups of a connected reductive algebraic group G,
over a ground field K. We parametrize their conjugacy classes in terms of sets
of simple roots and we prove that two Levi K-subgroups of G are rationally
conjugate if and only if they are geometrically conjugate.
These results are generalized to arbitrary connected linear algebraic
K-groups. In that setting the appropriate analogue of a Levi subgroup is
derived from the notion of a pseudo-parabolic subgroup
Closed G-structures on non-solvable Lie groups
We investigate the existence of left-invariant closed G-structures on
seven-dimensional non-solvable Lie groups, providing the first examples of this
type. When the Lie algebra has trivial Levi decomposition, we show that such a
structure exists only when the semisimple part is isomorphic to
and the radical is unimodular and centerless.
Moreover, we classify unimodular Lie algebras with non-trivial Levi
decomposition admitting closed G-structures.Comment: 13 pages, to appear in Revista Matematica Complutens
Modulo representations of reductive -adic groups: functorial properties
Let be a local field with residue characteristic , let be an
algebraically closed field of characteristic , and let be a
connected reductive -group. In a previous paper, Florian Herzig and the
authors classified irreducible admissible -representations of
in terms of supercuspidal representations of Levi subgroups
of . Here, for a parabolic subgroup of with Levi subgroup and an
irreducible admissible -representation of , we determine the
lattice of subrepresentations of and we show that
is irreducible for a general unramified character
of . In the reverse direction, we compute the image by the two
adjoints of of an irreducible admissible representation
of . On the way, we prove that the right adjoint of respects admissibility, hence coincides with Emerton's ordinary part functor
on admissible representations.Comment: 39 page
Twisted Levi Sequences and Explicit Styles on Sp(4)
Let G be a connected reductive group over a field F. A twisted Levi subgroup G0 of G is a reductive subgroup such that G' [circle times]F F[over-bar] is a Levi subgroup of G' [circle times]F F[over-bar]. Twisted Levi subgroups have been an important tool in studying the structure theory of representations of p-adic groups. For example, supercuspidal representations are built out of certain representations of twisted Levi subgroups ([20]), and Hecke algebra isomorphisms are established with Hecke algebras on twisted Levi subgroups, which suggests an inductive structure of representations (see [9] for example).National Science Foundation (U.S.). Focused Research Grou
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