Ph.D Thesis | |

Ph.D Student | Gurevich Maxim |
---|---|

Subject | On Distinguished Repesentations of P-Adic General Linear Groups |

Department | Department of Mathematics |

Supervisor | ASSOCIATE PROF. Omer Offen |

Full Thesis text |

The representation theory of reductive linear groups over non-Archimedean local fields has long been a topic of extensive research. It both complements the classical study of symmetry through Lie groups, and serves as a tool in modern formulations of number-theoretic problems.

An irreducible smooth representation
of a p-adic group *G* is said to be *H*-distinguished, for a subgroup
*H<G*, when there is a non-zero *H*-invariant linear form on the
representation. The *H*-distinguished representations of *G* are the
basic objects of harmonic analysis on the space *G/H*.

We treat two problems on
distinguished representations in cases where *G/H* is a p-adic symmetric
space and the group *G* is the general linear group.

In the first part, we let *E/F*
to be a quadratic extension of p-adic fields. We prove that every smooth
irreducible ladder representation of the group *GL _{n}(E)* which is
contragredient to its own Galois conjugate, possesses the expected distinction
properties relative to the subgroup

In the second part, we study the role
of the mirabolic subgroup *P* of *G = GL _{n}(F)* for smooth
irreducible representations of