双参数量子正交群和辛群的表示

Equivalences between three presentations of orthogonal and symplectic Yangians

We prove the equivalence of two presentations of the Yangian $Y(\mathfrak{g})$ of a simple Lie algebra $\mathfrak{g}$ and we also show the equivalence with a third presentation when $\mathfrak{g}$ is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians.

正交和辛量子矩阵代数及其Cayley-Hamilton定理

Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them

对于正交型和辛型量子矩阵（QM-）代数族，我们导出了相应的Cayley-Hamilton定理。对于更广泛的Birman-Murakami-Wenzl型QM-代数，我们研究了它的特征子代数（特征多项式的系数取值的子代数）的结构.定义了特征子代数的3组生成元，并导出了它们之间的递归Newton关系和Wronski关系。对于正交型QM-代数族，得到了特征子代数的生成元的附加互反关系。

正交辛量子群的两个外代数

Two Exterior Algebras for orthogonal and symplectic Quantum Groups

设Γ是正交或辛量子群O_q（N）或Sp_q（N）上的N^2维双共变一阶微分演算.参数q不是单位单位根。我们证明了第二反对称化子外代数是泛外代数U与w^2生成的主理想的商。这里w表示唯一的直到标量的双不变1-形式。此外，w^2是U的中心，U是一个内微分学。

Orthogonal and symplectic Yangians - linear and quadratic evaluations

Orthogonal or symplectic Yangians are defined by the Yang-Baxter $RLL$ relation involving the fundamental $R$ matrix with $so(n)$ or $sp(2m)$ symmetry. Simple $L$ operators with linear or quadratic dependence on the spectral parameter exist under restrictive conditions. These conditions are investigated in general form.

正交和辛李代数的量子群分类和Belavin-Drinfeld上同调

Classification of quantum groups and Belavin--Drinfeld cohomologies for orthogonal and symplectic Lie algebras

本文继续研究在arXiv：1303.4046 [math.QA]中引入的Belavin-Drinfeld上同调，它与准经典极限是给定的单复李代数的量子群的分类有关。在这里，我们计算Belavin-Drinfeld上同调的所有非反对称$r$ -矩阵从Belavin-Drinfeld列表的简单李代数类型$B$，$C$，和$D$。

顶点算子、Weyl行列式公式和Littlewood对偶

Vertex operators, Weyl determinant formulae and Littlewood duality

研究并推广了辛和正交Schur函数的顶点算子实现。给出了辛群和正交群的不可约特征标的行列式恒等式的新证明。利用顶点算子给出了泛正交Schur函数与辛Schur函数的对偶性的新证明。