Injective and Tilting Resolutions and a Kazhdan-Lusztig Theory for the General Linear and Symplectic Group

Abstract Let k be an algebraically closed field of characteristic p > 0 and let G a symplectic or general linear group over . We consider induced modules for under the assumption that is bigger than greatest hook length in partitions involved. give explicit constructions left resolutions by tilting modules. Furthermore, we injective certain truncated categories. show multiplicities indecomposable these are coefficients Kazhdan-Lusztig polynomials. also our categories have theory sense Cline, Parshall Scott. This builds further on work Cox-De Visscher Brundan-Stroppel.