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Drinfeld realisations are constructed for the quantum affine superalgebras of the series ${rmmathfrak{osp}}(1|2n)^{(1)}$,${rmmathfrak{sl}}(1|2n)^{(2)}$ and ${rmmathfrak{osp}}(2|2n)^{(2)}$. By using the realisations, we develop vertex operator representations and classify the finite dimensional irreducible representations for these quantum affine superalgebras.
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 integ
We obtain Drinfeld second realization of the quantum affine superalgebras associated with the affine Lie superalgebra $D^{(1)}(2,1;x)$. Our results are analogous to those obtained by Beck for the quantum affine algebras. Becks analysis uses heavily t
In this paper we study the first cohomologies for the following three examples of vertex operator algebras: (i) the simple affine VOA associated to a simple Lie algebra with positive integral level; (ii) the Virasoro VOA corresponding to minimal mode
In this paper, a notion of affine walled Brauer-Clifford superalgebras $BC_{r, t}^{rm aff} $ is introduced over an arbitrary integral domain $R$ containing $2^{-1}$. These superalgebras can be considered as affinization of walled Brauer superalgebras
In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related to the $p$-