Stable discrete series characters as lifts from complex two-structure groups
نویسندگان
چکیده
منابع مشابه
Stable Discrete Series Characters as Lifts from Complex Two-structure Groups
Let G ⊂ GC be a connected reductive linear Lie group with a Cartan subgroup B which is compact modulo the center of G. Then G has discrete series representations. Further, since G is linear the characters of discrete series representations can be averaged over the Weyl group to obtain stable discrete series characters which are constant on orbits of GC in G′, and can be regarded as the restrict...
متن کاملDiscrete Series Characters as Lifts from Two-structure Groups
Let G be a connected reductive Lie group with a relatively compact Cartan subgroup. Then it has relative discrete series representations. The main result of this paper is a formula expressing relative discrete series characters on G as “lifts” of relative discrete series characters on smaller groups called two-structure groups for G. The two-structure groups are connected reductive Lie groups w...
متن کاملStable Discrete Series Characters at Singular Elements
Write E for the stable discrete series character associated to an irreducible nite-dimensional representation E of a connected real reductive group G. Let M be the centralizer of the split component of a maximal torus T , and denote by M ( ; E) Arthur's extension of jDG M ( )j 12 E( ) to T (R). In this paper we give a simple explicit expression for M ( ; E), when is elliptic in G. We do not ass...
متن کاملDiscrete Series Characters and Two-structures
Let G be a connected semisimple real Lie group with compact Cartan subgroup. Harish-Chandra gave formulas for discrete series characters which are completely explicit except for certain interger constants appearing in the numerators. The main result of this paper is a new formula for these constants using two-structures. The new formula avoids endoscopy and stable discrete series entirely, expr...
متن کاملThe characters of the holomorphic discrete series.
This paper summarizes the derivation of an explicit and global formula for the character of any holomorphic discrete series representation of a reductive Lie group G which satisfies certain conditions. The only very restrictive condition is that G/K be a Hermitian symmetric space. (Here K is the maximal compact subgroup of G.).
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: 2000
ISSN: 0030-8730
DOI: 10.2140/pjm.2000.196.187