Representations of super Yangian
نویسنده
چکیده
We present in detail the classification of the finite dimensional irreducible representations of the super Yangian associated with the Lie superalgebra gl(1|1). 1 Introduction Many new algebraic structures were discovered in the study of soluble models in statistical mechanics and quantum field theory. Amongst them the quantum groups[1][2] and Yangians[3] are particularly interesting. The former have the structures of quasi triangular Hopf algebras, admitting universal R matrices which play important roles in many fields in both mathematical physics and pure mathematics. The Yangians have structures closely related to but distinct from that of the quantum groups. Their representation theory forms the basis of the quantum inverse scattering method. Recent research has also revealed that the Yangian structure is the underlying symmetry of many types of integrable models. For practical applications, e.g., using the algebraic Bethe Ansatz to diagonalize Hamiltonians of spin chains, one is primarily interested in the finite dimensional representations of Yangians. The systematic study of representations of the Yangians associated with ordinary Lie algebras was undertaken by Drinfeld[4], who, using techniques developed in Tarasov's work[5] on the gl(2) Yangian, obtained the necessary and sufficient conditions for irreps to be finite dimensional. The structures of the finite dimensional irreps of the gl(m) Yangian were extensively studied[6][7][8]; representations of so(n) and sp(2n) Yangians and the twisted Yangians were studied in [9] and [10]; and the fundamental irreps of all the Yangians were investigated by Chari and Pressley[11]. It is also possible to introduce Yangians[12] and their quantum analogues[13] associated with the simple Lie superalgebras, which we will call super Yangians in this paper. Their structures, and their connections with the Lie superalgebras and the 1
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تاریخ انتشار 1995