Local Newforms for GSp(4)

Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).

• Eigenvalue
• Newforms
• Node
• Representation theory
• Siegel
• algebraic number theory
• oldforms
• paramodular
• representations

From the reviews:

"This book gives an analog of Casselman’s local Atkin-Lehner theorem for GSp(4). … The local theory of the Novodvorsky construction is advanced by this work of Roberts and Schmidt, and the converse is also true: the Novodvorsky local integrals play an important role in the proof, especially in the supercuspidal case. … proves an important theorem, and moreover is written in a useful and instructive way." (Daniel Bump, Mathematical Reviews, Issue 2008 g)

• University of Idaho, 83844-1103, Moscow, USA

  Brooks Roberts

• University of Oklahoma, 73019-0315, Norman, USA

  Ralf Schmidt

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