ON TYPICAL REPRESENTATIONS FOR DEPTH-ZERO COMPONENTS OF SPLIT CLASSICAL GROUPS

Let G be a split classical group over a non-Archimedean local field F with the cardinality of the residue field q(F) > 5. Let M be the group of F-points of a Levi factor of a proper F-parabolic subgroup of G. Let [M,sigma(M)](M) be an inertial class such that sigma(M) contains a depth-zero Moy-Prasad type of the form (K-M, tau(M) ), where K-M is a hyperspecial maximal compact subgroup of M. Let K be a hyperspecial maximal compact subgroup of G(F) such that K contains K-M. In this article, we classify s-typical representations of K. In particular, we show that the s-typical representations of K are precisely the irreducible subrepresentations of ind(J)(K) lambda, where (J, lambda) is a level-zero G-cover of (K &AND M; tau(M)).