Duality and the normalization of standard intertwining operators

نویسنده

  • Chris Jantzen
چکیده

Normalized standard intertwining operators associated to an induced representation and its dual (dual in the sense ofAubert) arise in work on a conjecture ofArthur about R-groups. The purpose of this paper is to address the question of relating the normalizing factors used.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Caractérisation des paramètres d'Arthur‎, ‎une remarque

‎In The endoscopic classification of representations‎‎, ‎J‎. ‎Arthur has proved the Langlands' classification for discrete series of p-adic classical groups‎. ‎This uses endoscopy and twisted endoscopy‎. ‎In this very short note‎, ‎we remark that the normalization ‎$‎rm‎grave{a}‎$‎ la Langlands-Shahidi of the intertwining operators‎, ‎allows to avoid endoscopy‎. ‎This is based on the intertwini...

متن کامل

On the analytic properties of intertwining operators I‎: ‎global normalizing factors

‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key in...

متن کامل

The Action of Intertwining Operators on Spherical Vectors in the Minimal Principal Series of a Reductive Symmetric Space

We study the action of standard intertwining operators on H-fixed generalized vectors in the minimal principal series of a reductive symmetric space G/H of Harish-Chandra's class. The main result is that-after an appropriate normalization-this action is unitary for the unitary principal series. This is an extension of previous work under more restrictive hypotheses on G and H. The present resul...

متن کامل

On Invariants of Discrete Series Representations of Classical P -adic Groups

To an irreducible square integrable representation π of a classical p-adic group, C. Mœglin has attached invariants Jord(π), πcusp and ǫπ . These triples classify square integrable representations modulo cuspidal data (assuming a natural hypothesis). The definition of these invariants in [M] is rather simple in terms of induced representations, except at one case when a coherent normalization o...

متن کامل

DOUBLE HECKE ALGEBRAS 3 Nonsymmetric polynomials

0. Introduction 1. Affine Weyl groups (Reduction modulo W ) 2. Double Hecke algebras (Automorphisms, Demazure-Lusztig operators) 3. Macdonald polynomials (Intertwining operators) 4. Fourier transform on polynomials (Four transforms) 5. Jackson integrals (Macdonald’s η-identities) 6. Semisimple and pseudo-unitary representations (Main Theorem) 7. Spherical representations (Semisimple spherical r...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004