Jacobi-Hecke algebras and a rationality theorem for a formal Hecke series
type: Item
instance of: scholarly article
title: Jacobi-Hecke algebras and a rationality theorem for a formal Hecke series
zbMATH Open document ID: 0958.11034
author: Joachim Dulinski
published in: Manuscripta Mathematica
publication date: 2001-04-17T00:00:00Z
review text: In the paper under review the author develops a Hecke theory for the Jacobi group of degree \((1,m)\) over a local field of characteristic \(\neq 2\). In this case the symplectic group is always \(SL(2)\). Under a certain maximality condition the Hecke algebra is shown to decompose into a direct product of two algebras. The irregular component is finite-dimensional and semisimple. The Satake isomorphism maps the regular component onto the algebra of Laurent polynomials in one variable invariant under the Weyl group of \(SL(2,F)\). Finally a rationality theorem is derived for the Hecke series along the lines of \textit{S. Böcherer}'s proof [Abh. Math. Sem. Univ. Hamb. 56, 35-47 (1986; Zbl 0613.10026)].
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 1334555
zbMATH Keywords: Jacobi group
zbMATH Keywords: Hecke algebra
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Satake isomorphism
zbMATH Keywords: rationality theorem
reviewed by: Aloys Krieg
MaRDI profile type: Publication
full work available at URL: s002290050173
OpenAlex ID: W2052593580
DOI: 10.1007/S002290050173
description: scientific article; zbMATH DE number 1334555