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GLn(R) Action on Posn(R)

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

Abstract

Let G = GLn(R) or SLn(R) and Γn = GLn(Z). Let Posn(R) be the space of positive symmetric real n × n matrices. Recall that symmetric real n × n matrices Z have an ordering, defined by Z ≧ 0 if and only if 〈Zx, x〉 ≧ 0 for all xRn. We write Z1Z2 if and only if Z1 - Z2 ≧ 0. If Z ≧ 0 and Z is non-singular, then Z ≫ 0, and in fact Z ≧ λI if λ is the smallest, necessarily positive, eigenvalue.

Keywords

  • Fundamental Domain
  • Eisenstein Series
  • Diagonal Component
  • Coset Space
  • Inductive Construction

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© 2005 Springer-Verlag Berlin/Heidelberg

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Jorgenson, J., Lang, S. (2005). GLn(R) Action on Posn(R). In: Posn(R) and Eisenstein Series. Lecture Notes in Mathematics, vol 1868. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11422372_1

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