On the decomposition of reducible principal series representations ofp-adic Chevalley groups
نویسندگان
چکیده
منابع مشابه
Principal series representations of direct limit groups
We combine the geometric realization of principal series representations of [28] with the Bott–Borel–Weil Theorem for direct limits of compact groups found in [22], obtaining limits of principal series representations for direct limits of real reductive Lie groups. We introduce the notion of weakly parabolic direct limits and relate it to the conditions that the limit representations are norm–p...
متن کاملPrincipal Series Representations of Metaplectic Groups
We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order n. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.
متن کاملPrincipal Nilpotent Orbits and Reducible Principal Series
Let G be a split reductive p-adic group. In this paper, we establish an explicit link between principal nilpotent orbits of G and the irreducible constituents of principal series of G. A geometric characterization of certain irreducible constituents is also provided.
متن کاملDiscrete Series Representations of Unipotent p-adic Groups
For a certain class of locally profinite groups, we show that an irreducible smooth discrete series representation is necessarily supercuspidal and, more strongly, can be obtained by induction from a linear character of a suitable open and compact modulo center subgroup. If F is a non-Archimedean local field, then our class of groups includes the groups of F -points of unipotent algebraic group...
متن کاملEssays on representations of p-adic groups Smooth representations
A smooth G module over R is a representation (π, V ) of G on an R-module V such that each v in V is fixed by an open subgroup of G. A smooth representation (π, V ) is said to be admissible if for each open subgroupK in G the subspace V K of vectors fixed by elements of K is finitely generated overR. UsuallyRwill be a field (necessarily of characteristic 0) in which case this means just that V K...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1982
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1982.101.351