论文标题
关于非还原群的Hecke代数
On irreps of a Hecke algebra of a non-reductive group
论文作者
论文摘要
我们研究了这对$（{\ rm pgl} _2（f [ε] /（ε^2））的Hecke代数的不可约表示，{\ rm pgl} _2（\ rm pgl} _2（\ nathcal {o} {o} [o} [ε] /（ε] /（ε^2）） $ \ MATHCAL {O} \子集f $是其整数环。我们希望将我们的分析应用于Hecke操作员在cuspidal函数空间上的研究，该函数在主$ {\ rm pgl} _2 _2 $ - 在曲线上划分的曲线$ \ mathbb {f} _q [ε] /（ε] /（ε^2）$。
We study irreducible representations of the Hecke algebra of the pair $({\rm PGL}_2 (F[ε] / (ε^2)) , {\rm PGL}_2 (\mathcal{O}[ε] / (ε^2)))$ where $F$ is a local non-Archimedean field of characteristic different than $2$ and $\mathcal{O} \subset F$ is its ring of integers. We expect to apply our analysis to the study of the spectrum of Hecke operators on the space of cuspidal functions on the space of principal ${\rm PGL}_2$-bundles on curves over rings $\mathbb{F}_q [ε] / (ε^2)$.
