Base change for ramified unitary groups: the strongly ramified case
Abstract
We describe a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a padic field of odd residual characteristic. Roughly speaking, we require the underlying stratum of a given supercuspidal representation to be skew maximal simple, and the field datum of this stratum to be of maximal degree, tamely ramified over the base field, and quadratic ramified over its subfield fixed by the Galois involution that defines the unitary group. The base change of this supercuspidal representation is described by a canonical lifting of its underlying simple character, together with the base change of the levelzero component of its inducing cuspidal type, modified by a sign attached to a quadratic Gauss sum defined by the internal structure of the simple character. To obtain this result, we study the reducibility points of a parabolic induction and the corresponding module over the affine Hecke algebra, defined by the covering type over the product of types of the given supercuspidal representation and of a candidate of its base change.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.01316
 Bibcode:
 2020arXiv200101316B
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Representation Theory;
 22E50;
 11F70;
 11S37;
 20C08;
 20G25
 EPrint:
 30 pages