Ottawa Lectures on Admissible Representations of Reductive P-adic Groups

bijection Bruhat-Tits building Bruhat-Tits theory canonical Cartan involution centre character coefficients commutative compact open subgroup connected reductive constructible motivic functions cuspidal representation definable subassignment definition denote depth zero direct sum element example filtration follows formula functor G-subspace Gal(F/F GL(n Hence homomorphism induced irreducible cuspidal representation irreducible finite representations irreducible representations irreducible smooth representation irreducible subquotient Irrt isomorphism isomorphism classes Jacquet Langlands correspondence Lemma Levi component Levi subgroup Math maximal compact subgroup morphism motivic integration motivic volume Moy-Prasad non-Archimedean non-zero notation Note open compact ord(x p-adic field parabolic subgroup Plancherel progenerator proof Proposition prove quasi-character quotient reductive group reductive p-adic groups representation of G residue field root datum Section semisimple space split subgroup of G subquotient subset supercuspidal representations Suppose surjective tamely ramified Theorem Tits topology torus trivial unique unramified valuation valued field variables Xnr G