R -Groups and elliptic representations for similitude groups
نویسندگان
چکیده
منابع مشابه
R-groups and Elliptic Representations for Similitude Groups
The tempered spectrum of the similitude groups of non-degenerate symplectic, hermitian, or split orthogonal forms defined over p-adic groups of characteristic zero is studied. The components of representations induced from discrete series of proper parabolic subgroups are classified in terms of R-groups. Multiplicity one is proved. The tempered elliptic spectrum is identified, and the relation ...
متن کاملQUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
متن کاملA note on orthogonal similitude groups
Let V be a vector space over the field F such that charðF Þ 61⁄4 2, and let V have a symmetric nondegenerate bilinear form. Let GOðV Þ be the orthogonal similitude group for this symmetric form, with similitude character . We prove that if g 2 GOðV Þ with ðgÞ 1⁄4 , then g 1⁄4 t1t2 where t1 is an orthogonal involution, and t2 is such that t 2 2 1⁄4 I and ðt2Þ 1⁄4 . As an application, we obtain a...
متن کاملBehavior 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 کاملPower Operations in Elliptic Cohomology and Representations of Loop Groups
The first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve. The second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups. The third part investigates the representation theoretic considerations which give rise to the power operations discussed in the first part.
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: Mathematische Annalen
سال: 1997
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s002080050051