Tight Monomials With7≤t≤10in Quantum Group For Type A₅

Recently years, quantum group (i.e., quantized enveloping algebra) is a hot re-search topic in algebra field. Quantum group has a basis which is called Canonical basis as a Q(v)-vector space, which plays an important role in the theory of the quan-tum groups and their representations, also is a powerful tool to study quantum groups and their representations. Many mathematicians in algebra field devote themself to determine elements in Canonical basis, which the key is to determine monomials in Canonical basis (so called tight monomials). All of tight monomials with7≤t-value <10in quantum group for type A5are completely determined in this paper.This paper is divided into four chapters, organized as follows:In the first chapter, survey of quantum group is introduced and the problems of this paper is put forward.In the second chapter, we review the related concepts of quantum group, and the algebraic definition of Canonical basis of quantum group.In the third chapter, we list the existed results of Canonical basis of quantum group, review the related concepts of quiver and introduce the discriminant method of tight monomials of Canonical basis.In the fourth chapter, we give all the tight monomials with7≤t-value≤10in quantum group for type A5.