Principal series representations of finite Chevalley groups
نویسندگان
چکیده
منابع مشابه
Small degree representations of finite Chevalley groups in defining characteristic
We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l our bound is proportional to l3 and for rank 11 m...
متن کاملPrincipal 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 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: Journal of Algebra
سال: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90149-7