Local Newforms for GSp(4)
Roberts, Brooks.
Local Newforms for GSp(4) [electronic resource] / by Brooks Roberts, Ralf Schmidt. - VIII, 312 p. online resource. - Lecture Notes in Mathematics, 1918 0075-8434 ; . - Lecture Notes in Mathematics, 1918 .
A Summary -- Representation Theory -- Paramodular Vectors -- Zeta Integrals -- Non-supercuspidal Representations -- Hecke Operators -- Proofs of the Main Theorems.
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).
9783540733249
10.1007/978-3-540-73324-9 doi
Number theory.
Algebra.
Topological Groups.
Number Theory.
Algebra.
Topological Groups, Lie Groups.
QA241-247.5
512.7
Local Newforms for GSp(4) [electronic resource] / by Brooks Roberts, Ralf Schmidt. - VIII, 312 p. online resource. - Lecture Notes in Mathematics, 1918 0075-8434 ; . - Lecture Notes in Mathematics, 1918 .
A Summary -- Representation Theory -- Paramodular Vectors -- Zeta Integrals -- Non-supercuspidal Representations -- Hecke Operators -- Proofs of the Main Theorems.
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).
9783540733249
10.1007/978-3-540-73324-9 doi
Number theory.
Algebra.
Topological Groups.
Number Theory.
Algebra.
Topological Groups, Lie Groups.
QA241-247.5
512.7