On local gamma factors for orthogonal groups and unitary groups

نویسندگان

  • S‎. ‎ Rallis
چکیده مقاله:

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of spherical Bessel models‎. 

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Local models for ramified unitary groups

S′ −−−−→ Spec(OE) is cartesian. To qualify as a model, the scheme S′ should at least be flat over Spec(OE) and have only “good” singularities. In the PEL-case, S can be written as a moduli space of abelian varieties with polarization, an action by a semisimple Q-algebra and a K-level strucure where K ⊂ G(Af ) is an open and compact subgroup. If we fix a prime p , the investigation of a model S′...

متن کامل

Local Theta Correspondence for Small Unitary Groups

In this paper we give an explicit parameterization of the local theta correspondence of supercuspidal representations for the reductive dual pairs (U1(F ),U1(F )), (U1(F ),U1,1(F )), (U1(F ),U2(F )), and (U1(F ),U1,2(F )) of unitary groups over a nonarchimedean local field F of odd residue characteristic.

متن کامل

Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...

متن کامل

Orthogonal Groups over Local Rings

In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...

متن کامل

Word Measures on Unitary Groups

We combine concepts from random matrix theory and free probability together with ideas from the theory of commutator length in groups and maps from surfaces, and establish new connections between the two. More particularly, we study measures induced by free words on the unitary groups U (n). Every word w in the free group Fr on r generators determines a word map from U (n) to U (n), defined by ...

متن کامل

Theta Correspondence for Unitary Groups

In this paper we study the theta correspondence for Unitary groups of the same size over local and global fields. This correspondence has been studied in many cases by several authors. We are able to unify and generalise all these known results in terms of two conjectures, one local and the other global. These conjectures are in terms of the parametrisation of irreducible admissible representat...

متن کامل

منابع من

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

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 43  شماره Issue 4 (Special Issue)

صفحات  387- 403

تاریخ انتشار 2017-08-30

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023