Unicity of types for supercuspidals

Vytautas Paskunas

paper

Unicity of types for supercuspidals

arXiv:math/0306124

Abstract

Let $F$ be a non-Archimedean local field, with the ring of integers $o_{F} . L e t$ G=GL_N(F) $,$ K=GL_N(\mathfrak{o}_F) $an d$ π $a s u p er c u s p i d a l r e p r ese n t a t i o n o f$ G $. W es h o w t ha tt h er ee x i s t a u ni q u e i r r e d u c ib l es m oo t h r e p r ese n t a t i o n$ τ $o f$ K $, s u c h t ha tt h er es t r i c t i o n t o$ K $o f a s m oo t hi r r e d u c ib l er e p r ese n t a t i o n$ π' $o f$ G $co n t ain s$ τ $i f an d o n l y i f$ pi' $i s i so m or p hi c t o$ π\otimesχ\circ\det $, w h er e$ χ $i s an u n r ami f i e d q u a s i c ha r a c t er o f$ F^{\times} $. M or eo v er, w es h o w t ha t$ π $co n t ain s$ τ$ with the multiplicity 1. As a corollary we obtain a kind of inertial local Langlands correspondence.

42 pages

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