Vertex operator representations of quantum affine superalgebras

2017/07/28 by Xu, Ying, Zhang, Ruibin
#17B37 #17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1707.09140

Abstract

Let Uq(g) be the quantum affine superalgebra associated with an affine Kac-Moody superalgebra g which belongs to the three series osp(1|2n)^(1),sl(1|2n)^(2) and osp(2|2n)^(2). We develop vertex operator constructions for the level 1 irreducible integrable highest weight representations and classify the finite dimensional irreducible representations of Uq(g). This makes essential use of the Drinfeld realisation for Uq(g), and quantum correspondences between affine Kac-Moody superalgebras, developed in earlier papers.

Related

• Drinfeld realisations and vertex operator representations of quantum affine superalgebras
• Level One Representations of Quantum Affine Algebras U_q(C⁽¹⁾_n)
• Vertex operators and 2-representations of quantum affine algebras
• Level one representations of U_q(G₂⁽¹⁾)
• Drinfeld realisations of quantum affine superalgebras