We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
from I - Hypotheses, automorphic forms, constant terms
Published online by Cambridge University Press: 22 September 2009
Hypotheses and general notation
Definitions
Let k be a global field and be the ring of adeles of k. For a finite place v of k, we write for the ring of integers. Let be the ring of finite adeles of k and, the product being over the archimedean places. If k is a function field, let q be the number of elements of its field of constants.
Let G be a connected reductive algebraic group defined over k. Fix an embedding into a linear group as follows. First choose an embedding, defined over k, with closed image. Then iG: G ↪ GL2n is defined by
There exists a finite set S of places of k, containing the archimedean places, such that the image of iG is defined and smooth over (see [Sp] §4.9). For v ∉ S, this allows us to define the group of points with values in. For almost all v ∉ S, this is a maximal compact subgroup of G(kv) (see [Sp] p.18, 1.3 and what follows). We fix a compact maximal subgroup K of G() such that K = ΠυKν product over all places of k, where Kν is a maximal compact subgroup of G(kυ). We suppose, as we may, that for almost all finite places. We will impose further properties on K in I.1.4.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
