Beta extensions and cuspidal types for p-adic spin groups

Abstract

Let $$\widehat{G}$$ be a spin group over a locally compact non-archimedean local field F of odd residual characteristic. When F has characteristic zero we define $$\beta $$ -extensions of the semisimple characters for $$\widehat{G}$$ . Then we contruct cuspidal types for many new supercuspidal representations of $$\widehat{G}$$ .