A quantum fermion realisation of the finite dimensional spinor representation of ${\rm{U}}_q({\mathfrak {osp}}(1|2n))$

Drinfeld realisations of quantum affine superalgebras

We construct Drinfeld realisations for the quantum affine superalgebras associated with the osp(1|2n)^{(1)}, Sl(1|2n)^{(2)} and osp(2|2n)^{(2)} series of affine Lie superalgebras.

Drinfeld realisations and vertex operator representations of quantum affine superalgebras

Drinfeld realisations are constructed for the quantum affine superalgebras of the series ${\rm\mathfrak{osp}}(1|2n)^{(1)}$,${\rm\mathfrak{sl}}(1|2n)^{(2)}$ and ${\rm\mathfrak{osp}}(2|2n)^{(2)}$. By using the realisations, we develop vertex operator representations and classify the finite dimensional irreducible representations for these quantum affine superalgebras.

可容许能级 $\mathfrak{osp}(1|2)$ 极小模型及其松弛最高权模

Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modules

本文结合两类自由场实现、屏蔽算子与 Jack 基对称函数理论，计算 Zhu 代数表示，并分类 Neveu-Schwarz 与 Ramond 扇区中的 $\mathfrak{osp}(1|2)$ 极小模型单松弛最高权模。

Vertex operator representations of 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 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.

Super Yangian Y（osp（1| 2））及其量子偶的泛R-矩阵

Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double

我们提出了超级Yangian Y（osp（1）的Drinfel'd实现|2）），包括余积的显式表达式。我们特别表明，有必要引入补充塞尔关系。进行了量子双光子的构建。这使得我们能够给出DY（osp（1））的泛R-矩阵|（2））。

A realisation of the Bershadsky--Polyakov algebras and their relaxed modules

We present a realisation of the universal/simple Bershadsky--Polyakov vertex algebras as subalgebras of the tensor product of the universal/simple Zamolodchikov vertex algebras and an isotropic lattice vertex algebra. This generalises the realisation of the universal/simple affine vertex algebras associated to $\mathfrak{sl}_2$ and $\mathfrak{osp}(1|2)$ given in arXiv:1711.11342. Relaxed highest-weight modules are likewise constructed, conditions for their irreducibility are established, and their characters are explicitly computed, generalising the character formulae of arXiv:1803.01989.