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
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© 2005 Springer-Verlag Berlin/Heidelberg
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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
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DOI: https://doi.org/10.1007/11422372_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25787-5
Online ISBN: 978-3-540-31548-3
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