P -Cuspidal Representations
Copyright policy )P -Cuspidal Representations
Let \({\mathbb{G}}\) be a reductive algebraic group over a non-archimedean local field k and \(G={\mathbb{G}}(k)\). This paper develops the work of \textit{H. Carayol} [Ann. Sci. Ec. Norm. Supér., IV. Sér. 17, 191-225 (1984; Zbl 0549.22009)] where certain supercuspidal representations of \(GL_ n\) were defined and studied with the help of certain parahoric subgroups and the so-called s-cuspidal elements. The author considers any parahoric subgroup P and P-cuspidal elements in \({\mathfrak g}*\) which are the analogues of s-elements. Here \({\mathfrak g}\) is the Lie algebra of G. He shows that if P is hyperspecial parahoric then (roughly speaking) the supercuspidal representations constructed from unramified elliptic tori come from P-cuspidal elements. The case when P is an Iwahori subgroup is given special consideration.
- Clarke University United States
non-archimedean local field, Lie algebra, Lie algebras of Lie groups, s-cuspidal elements, elliptic tori, Representations of Lie and linear algebraic groups over local fields, Langlands-Weil conjectures, nonabelian class field theory, Iwahori subgroup, Analysis on \(p\)-adic Lie groups, reductive algebraic group, parahoric subgroups, supercuspidal representations
non-archimedean local field, Lie algebra, Lie algebras of Lie groups, s-cuspidal elements, elliptic tori, Representations of Lie and linear algebraic groups over local fields, Langlands-Weil conjectures, nonabelian class field theory, Iwahori subgroup, Analysis on \(p\)-adic Lie groups, reductive algebraic group, parahoric subgroups, supercuspidal representations
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