Some Research On Specht Modules Of S_n And Presentations Of The Symmetric Inverse Semigroups

In associative algebra representations theory,group representations theory is an important branch of research,among them,the construction of the irreducible represen-tations of a group,and the study of its structure and related properties is the most basic and important topic.Similarly,in the field of the semigroups research,the presentations of semigroups is also an important research content.This paper is divided into two parts:In the first part,we discussed the irreducible representations of the symmetric group Sn on the complex field,also known as the Specht modules.The process of constructing the Specht modules with Young tableaux is given,and based on the known construction methods and the irreducible representations,we further give the internal structure and equivalent descriptions of the Specht module.In the second part,for the An type Dynkin diagram equipped with two special freezing points in cluster algebras,denoted by An1,2,we discussed the relationships between the mutations of An1,2 quivers and the presentations of the symmetric inverse semigroups In-1.We discussed the mutation equivalent class of An1,2 quivers,and a new definition of presentations of In-1 is given based on this mutation equivalent class,and proved that this definition is compatible with the mutations of An1,2 quivers.