Quantum Schur Algebras With Three Parameters And L Quantum Groups

In this thesis we mainly study the quantum Schur algebra corresponding to the Hecke algebra of affine type C with three parameters and its relation with the iquantum group of type jj.Firstly,the paper discusses the combinatorial properties of the Weyl group of affine type C,gives the(truncated)length functions on the affine Weyl group by using the information about matrices,and proves some quantum combinatorial equations.Secondly,the definitions of the Hecke algebra of affine type C with three parameters and the quantum Schur algebra corresponding to it are given.Then a rough multiplication formula in affine quantum Schur algebra is obtained.Finally,with the help of this multiplication formula,it is proved that there is an homomorphism from the iquantum group of type jj to the affine Schur algebra of affine type C with three parameters.