Affine quantum Schur algebras and affine Hecke algebras

الأصل · EN

Let F be the Schur functor from the category of finite dimensional H(r)C-modules to the category of finite dimensional S(n,r)C-modules, where H(r)C is the extended affine Hecke algebra of type A over C and S(n,r)C is the affine quantum Schur algebras over C. The Drinfeld polynomials associated with F(V) were determined in [7.6]CP96 and [4.4.2]DDF in the case of n>r, where V is an irreducible H(r)C-module. We will generalize the result in [loc. cit.] to the case of n≤ r. As an application, we will classify finite dimensional irreducible S(n,r)C-modules, which has been proved in [4.6.8]DDF using a different method. Furthermore we will use it to generalize [(6.5f)]Gr80 to the affine case.