Drinfeld Realization And Vertex Representation Of An Admissible Quantum Affine Algebra Of Typea₁⁽¹⁾

In 2020,Ge Feng,Naihong Hu,Rushu Zhuang constructed one class of new admissible quantum affine algebras A1(1).This paper is based on the above research.In this paper,the first major purpose is to establish a concrete isomorphism between the new class of quantum affine algebra of Uq(?)Jimbo Presentation and Drinfeld Presentation.The main method is to obtain the Drinfeld generators and the corresponding Drinfeld relations by using braid group action.The second purpose of the article is to construct vertex representation theory of Uq(?).The characteristics of Drinfeld relations,especially Heisenberg-Clifford relation,The indices are divided into odd and even parts to construct corresponding vertex operators,then vertex representations can be established on Fock space.In the meantime,we can prove that they satisfy Drinfeld relations.Finally,the vertex representations of odd and even are concatenated in a reasonable way to get the whole vertex representation.