SMOOTH REPRESENTATIONS OF GL(m) (D) V: ENDO-CLASSES

作者：Broussous P^*; Secherre V; Stevens S

来源：Documenta Mathematica, 2012, 17: 23-77.

• representations of p-adic groups
• simple characters
• type theory
• Shintani lift
• Jacquet-Langlands correspondence

Let F be a locally compact nonarchimedean local field. In this article, we extend to any inner form of GL(n) over F, with n %26gt;= 1, the notion of endo-class introduced by Bushnell and Henniart for GL(n) (F). We investigate the intertwining relations of simple characters of these groups, in particular their preservation properties under transfer. This allows us to associate to any discrete series representation of an inner form of GL(n) (F) an endo-class over F. We conjecture that this endo-class is invariant under the local Jacquet-Langlands correspondence.

• 出版日期2012