Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces (eBook)

Nicole Bopp (Autor)

eBook Download: PDF

233 Seiten
American Mathematical Society (Verlag)
978-1-4704-0422-2 (ISBN)

Infos

The aim of this paper is to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces. These symmetric spaces are obtained as follows. We consider a graded simple real Lie algebra $/widetilde{/mathfrak g}$ of the form $/widetilde{/mathfrak g}=V^-/oplus /mathfrak g/oplus V^+$, where $[/mathfrak g,V^+]/subset V^+$, $[/mathfrak g,V^-]/subset V^-$ and $[V^-,V^+]/subset /mathfrak g$. If the graded algebra is regular, then a suitable group $G$ with Lie algebra $/mathfrak g$ has a finite number of open orbits in $V^+$, each of them is a realization of a symmetric space $G / H_p$. The functional equation gives a matrix relation between the local zeta functions associated to $H_p$-invariant distributions vectors for the same minimal spherical representation of $G$. This is a generalization of the functional equation obtained by Godement} and Jacquet for the local zeta function attached to a coefficient of a representation of $GL(n,/mathbb R)$.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 1-4704-0422-2 / 1470404222
• ISBN-13: 978-1-4704-0422-2 / 9781470404222