The Hecke algebras for the orthogonal group SO(2,3) and the paramodular group of degree 2
| Autor: | Jonas Gallenkämper, Aloys Krieg |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Hecke algebra Algebra and Number Theory Group (mathematics) Mathematics::Number Theory Computer Science::Information Retrieval Polynomial ring 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Normal extension Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 010103 numerical & computational mathematics 01 natural sciences Tensor product Quadratic form Computer Science::General Literature Orthogonal group Isomorphism 0101 mathematics Mathematics |
| Zdroj: | International Journal of Number Theory. 14:2409-2423 |
| ISSN: | 1793-7310 1793-0421 |
| DOI: | 10.1142/s1793042118501464 |
| Popis: | In this paper, we consider the integral orthogonal group with respect to the quadratic form of signature [Formula: see text] given by [Formula: see text] for square-free [Formula: see text]. The associated Hecke algebra is commutative and also the tensor product of its primary components, which turn out to be polynomial rings over [Formula: see text] in two algebraically independent elements. The integral orthogonal group is isomorphic to the paramodular group of degree [Formula: see text] and level [Formula: see text], more precisely to its maximal discrete normal extension. The results can be reformulated in the paramodular setting by virtue of an explicit isomorphism. The Hecke algebra of the non-maximal paramodular group inside [Formula: see text] fails to be commutative if [Formula: see text]. |
| Databáze: | OpenAIRE |
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