Ottawa Lectures on Admissible Representations of Reductive P-adic Groups

abelian extension affine algebraic group 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 defined definition denote different direct sum element example filtration finite first follows formula functor G-subspace Grothendieck ring Hence homomorphism induced irreducible representations irreducible smooth representation irreducible subquotient isomorphism classes Langlands correspondence Lemma Let G Levi component Levi subgroup maximal compact subgroup module morphism motivic integration motivic volume Moy-Prasad non-Archimedean non-zero notation open compact p-adic p-adic field p-adic groups parabolic subgroup Plancherel progenerator proof Proposition prove quantifiers quasi-character quotient reductive group representation of G residue field root datum Rs(G Section semisimple space split subgroup of G subquotient subset supercuspidal representations Suppose surjective tamely ramified Theorem topology torus trivial unique unramified valuation valued field variables Weil group