Non-admissible representations for GL_2 over a p-adic field

2022-11-03   (16:00 ~ 17:00)
Building 108, Room 318
  • Speaker: Eknath Ghate (TIFR)

  • Title:Non-admissible representations for GL_2 over a p-adic field

  • Abstract:

The notion of admissibility is central in the theory of representations of reductive groups. It means that the space of vectors fixed by compact open subgroups is finite dimensional. In the global case (and in characteristic 0) it is related to the finite dimensionality of the space of automorphic forms of a fixed level (and weight).

In the local case, it is know that every smooth irreducible mod p representation of GL_2 over a p-adic field F is admissible if F = Q_p. In this talk we shall construct non-admissible_ smooth irreducible mod p representations of GL_2(F) if the residue field of F is a proper extension of F_p. This is joint work with Daniel Le and Mihir Sheth (and extends work of Le and Ghate-Sheth for F/Q_p unramified).