Principal series representations of direct limit 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 Series Representations of Metaplectic Groups over Local Fields
Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension G̃ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for G̃ and its applications to the study of Hecke algebras via a Satake is...
متن کاملModular Principal Series Representations
Recently, there has been considerable progress in classifying the irreducible representations of Iwahori–Hecke algebras at roots of unity. Here, we present an application of these results to l-modular Harish–Chandra series for a finite group of Lie type G(q). Under some mild condition on l, we show that the l-modular principal series representations of G(q) are naturally parametrized by a subse...
متن کاملGeneralized Baer-Invariant of a Pair of Groups and the Direct Limit
In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...
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: Compositio Mathematica
سال: 2005
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x05001430