QUANTUM WEYL RECIPROCITY AND TILTING MODULES

Quantum Weyl reciprocity relates the representation theory of Hecke al gebras of type A with that of q-Schur algebras. This paper establishes that Weyl reciprocity holds integrally (i. e., over the ring Z[q, q(- 1)] of Laurent polynomials) and that it behaves well under base-change . A key ingredient in our approach involves the theory of tilting modu les for q-Schur algebras. New results obtained in that direction inclu de an explicit determination of the Ringel dual algebra of a q-Schur a lgebra in all cases. In particular, in the most interesting situation, the Ringel dual identifies with a natural quotient algebra of the Hec ke algebra.