56 research outputs found
Resolutions for principal series representations of p-adic GL(n)
Let F be a nonarchimedean locally compact field with residue characteristic p
and G(F) the group of F-rational points of a connected reductive group.
Following Schneider and Stuhler, one can realize, in a functorial way, any
smooth complex finitely generated representation of G(F) as the 0-homology of a
certain coefficient system on the semi-simple building of G(F). It is known
that this method does not apply in general for smooth mod p representations of
G(F), even when G= GL(2). However, we prove that a principal series
representation of GL(n,F) over a field with arbitrary characteristic can be
realized as the 0-homology of the corresponding coefficient system
An inverse Satake isomorphism in characteristic p
Let F be a local field with finite residue field of characteristic p and k an
algebraic closure of the residue field. Let G be the group of F-points of a
F-split connected reductive group. In the apartment corresponding to a chosen
maximal split torus of T, we fix a hyperspecial vertex and denote by K the
corresponding maximal compact subgroup of G. Given an irreducible smooth
k-representation of K, we construct an isomorphism from the affine
semigroup k-algebra of the dominant cocharacters of T onto the Hecke algebra
. In the case when the derived subgroup of G is simply connected,
we prove furthermore that our isomorphism is the inverse to the Satake
isomorphism constructed by Herzig
Modules simples en caracteristique p des algebres de Hecke affines de type A_2
Soit F un corps local non archimedien de caracteristique residuelle p. On
designe par R un corps algebriquement clos de caracteristique p et par Q une
cloture algebrique du corps des nombres p-adiques. On classifie les modules
simples de dimension finie de la R-algebre de Hecke-Iwahori du groupe lineaire
Gl_3(F). Ils sont obtenus par reduction modulo p des modules simples de la
Q-algebre de Hecke-Iwahori qui possedent une structure entiere
Modules universels de GL(3) sur un corps p-adique en caract\'eristique p
Let F be a p-adic field with residue class field k. We investigate the
structure of certain mod p universal modules for GL(3,F) over the corresponding
Hecke algebras. To this end, we first study the structure of some mod p
universal modules for the finite group GL(n,k) as modules over the
corresponding Hecke algebras. We then relate this finite case to the p-adic one
by using homological coefficient systems on the the affine Bruhat-Tits building
of GL(3). Suppose now that k has cardinality p. We prove that the mod p
universal module of GL(3,F) relative to the Iwahori subroup is flat and
projective over the Iwahori-Hecke algebra. When replacing the Iwahori subgroup
of GL(3,F) by its pro-p-radical, we prove that the corresponding module is flat
over the pro-p Iwahori-Hecke algebra if and only if p=2
Pseudo-Goldstone magnons in the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4 with a pyrochlore magnetic sublattice
Low-energy spin excitations in any long-range ordered magnetic system in the
absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating
from the ordering wave vectors. In helimagnets, these modes hybridize into the
so-called helimagnon excitations. Here we employ neutron spectroscopy supported
by theoretical calculations to investigate the magnetic excitation spectrum of
the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in
which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated
pyrochlore sublattice. Apart from the conventional Goldstone mode emanating
from the (0 0 q) ordering vector, low-energy magnetic excitations in the
single-domain proper-screw spiral phase show soft helimagnon modes with a small
energy gap of ~0.17 meV, emerging from two orthogonal wave vectors (q 0 0) and
(0 q 0) where no magnetic Bragg peaks are present. We term them
pseudo-Goldstone magnons, as they appear gapless within linear spin-wave theory
and only acquire a finite gap due to higher-order quantum-fluctuation
corrections. Our results are likely universal for a broad class of symmetric
helimagnets, opening up a new way of studying weak magnon-magnon interactions
with accessible spectroscopic methods.Comment: V3: Final version to be published in Phys. Rev.
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