Langlands Reciprocity for C ∗-Algebras
| Autor: | Igor Nikolaev |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Shimura variety
Automorphic L-function Mathematics::Number Theory 010102 general mathematics 0102 computer and information sciences Langlands dual group Reductive group Algebraic number field 01 natural sciences Combinatorics Algebra Langlands program 010201 computation theory & mathematics Local Langlands conjectures Irreducible representation 0101 mathematics Mathematics::Representation Theory Mathematics |
| Zdroj: | Operator Theory, Functional Analysis and Applications ISBN: 9783030519445 |
| DOI: | 10.1007/978-3-030-51945-2_26 |
| Popis: | We introduce a C∗-algebra \({\mathcal A}_V\) of a variety V over the number field K and a C∗-algebra \({\mathcal A}_G\) of a reductive group G over the ring of adeles of K. Using Pimsner’s Theorem, we construct an embedding \({\mathcal A}_V\hookrightarrow {\mathcal A}_G\), where V is a G-coherent variety, e.g. the Shimura variety of G. The embedding is an analog of the Langlands reciprocity for C∗-algebras. It follows from the K-theory of the inclusion \({\mathcal A}_V\subset {\mathcal A}_G\) that the Hasse-Weil L-function of V is a product of the automorphic L-functions corresponding to irreducible representations of the group G. |
| Databáze: | OpenAIRE |
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