Representations of GL(2) and SL(2) over finite fields
نویسنده
چکیده
Irreducible complex representations of GL(2) and SL(2) over a finite field can be classified by methods useful for p-adic reductive groups and real Lie groups. (See Piatetski-Shapiro’s inspiring A.M.S. Memoir on this subject.) That is, we first see that most principal series representations are irreducible. We determine the irreducible constituents of the irregular principal series. We prove the uniqueness of Whittaker models by showing that the endomorphism ring of the space of Whittaker functions is commutative.
منابع مشابه
Globally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change, I : Iwasawa algebras and a base change map
This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2, mathbb{Z}_p)$. It then describes a natural base change map between the Iwasawa algebras or more correctly, as it turns out, between the global distribut...
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