Skip to main content

Measures, Integration and Quadratic Model

  • 739 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1868)

Abstract

We shall give various formulas related to measures on GLn and its subgroups. We also compute the volume of a fundamental domain, a computation which was originally carried out by Minkowski. Essentially we follow Siegel’s proof [Sie 45]. We note historically that people used to integrate over fundamental domains, until Weil pointed out the existence of a Haar (invariant) measure on homogeneous spaces with respect to unimodular subgroups in his book [We 40], and observed that Siegel’s arguments could be cast in the formalism of this measure [We 46].

Keywords

  • Invariant Measure
  • Homogeneous Space
  • Haar Measure
  • Fundamental Domain
  • Regular Element

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2005 Springer-Verlag Berlin/Heidelberg

About this chapter

Cite this chapter

Jorgenson, J., Lang, S. (2005). Measures, Integration and Quadratic Model. In: Posn(R) and Eisenstein Series. Lecture Notes in Mathematics, vol 1868. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11422372_2

Download citation