Skip to main content Accessibility help
×
Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-10T15:57:00.906Z Has data issue: false hasContentIssue false

Disconnected linear groups and restrictions of representations

Published online by Cambridge University Press:  06 January 2010

William M. Kantor
Affiliation:
University of Oregon
Lino Di Martino
Affiliation:
Università degli Studi di Milano
Get access

Summary

INTRODUCTION

In, Dynkin, Seitz and Testerman classified the maximal closed connected subgroups of the simple algebraic groups over an algebraically closed field K of characteristic p ≥ 0. The hard part of their analyses, for subgroups of the groups of classical type, concerns an irreducible, closed, connected subgroup G of SL(V) for some K-vector space V. They determine explicitly all possibilities for closed connected overgroups Y of G in I(V) (where I(V) = SL(V), SO(V), or Sp(V) depending upon the form on V preserved by G); the results appear in tables giving the high weights of the modules V|G and V|Y.

The question of inclusion relations among irreducible subgroups of SL(V), in addition to having implications for the subgroup structures of classical groups, is of interest in its own right. In this paper we present some recent results concerning this question when we allow subgroups that are not connected (the full proofs may be found in). Specifically, in Sections 2 and 3 we discuss the structure and some of the methods of the proof of Theorem 1. Let G be a non-connected algebraic group with simple identity component X. Let V be an irreducible KG-module with restricted X-high. weight(s).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org 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.

Available formats
×

Save book 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 Dropbox.

Available formats
×

Save book to Google Drive

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.

Available formats
×