On the local Langlands and Jacquet�Langlands correspondences
- Autores: Guy Henniart
- Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé
, Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 1171-1182 - Idioma: inglés
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Resumen
Let F be a locally compact non Archimedean field, and D a division algebra with centre F and finite dimension d2 over F. Fix an integer r 1, and let G = GLn(F ), G = GLr(D), where n = rd. Smooth irreducible representations of G are related to those of G via the Jacquet�Langlands correspondence, whereas the Langlands correspondence relates such representations of G to degree n representations of the absolute Galois group of F. We review some recent results on those correspondences, in particular on their explicit description.
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