Teoría de representaciones de grupos locales
Profesor: YUVAL FLICKER (Ohio State University)
Puntaje: 2 puntos (Lic. y Prof.)
Correlatividades: Álgebra III - Recomendable haber cursado Teoría de números, Grupos y álgebras de Lie.
Carga horaria: 5 horas por semana (durante junio y julio)
Carreras: Licenciatura en Matemática (Or. Pura y Aplicada), Profesorado en Matemática, Doctorado en Matemática
Breve descripción del curso:
The course will be an exposition to the theory of representations of p-adic linear algebraic groups G. These are infinite dimensional representations which are the local components of automorphic representations. I shall start from almost nothing, but I hope to reach the Bernstein center of the category of smooth representations of G, and explain some of its applications.
Elementary introduction to local spaces. Functions, distributions, sheaves. The Hecke algebra. Adjoint functors, induction, coinvariants. Decomposing categories by irreducible representations. Compact and cuspidal representations. Structure of linear algebraic groups. The other adjoint of the induction functor. The center of the category of smooth representations. Intertwining operators. Unitary representations. Square integrable and tempered representations. Cohomological dimension and duality.
Bibliografía
- Bernstein, I. N.; Zelevinsky, A. V. Induced representations of reductive p-adic groups. I. Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 441--472. Link
- J. N. Bernstein, Deligne, P. Le "centre" de Bernstein, Représentations des groupes réductifs sur un corps local. Travaux en Cours. Hermann, Paris, 1984. ii+157 pp.
- Bernstein, I. N.; Zelevinsky, A. V. Representation of the group GL(n,F) where F is a non-Archimedean local field. Uspekhi Mat. Nauk 31:3 (1976) Link
Reunión preliminar:
Aula y horario:
