广义仿射李代数$\widetilde{\frak{gl}_{2}(\bc_q)}$的厄米特表示

广义仿射李代数$\widetilde{\frak{gl}_{3}(\bc_q)}$的酉表示

Unitary representations of the extended affine Lie algebra $\widetilde{\frak{gl}_{3}(\bc_q)}$

利用自由域的思想给出了广义仿射李代数$\widetilde{\frak{gl}_{3}(\bc_q)}$的模.给出了模是酉模的一个充要条件。

广义仿射李代数$\widetilde{\frak{gl}_l({\mathbb{C}_q})}$的一类不可约模

A Class of Irreducible Modules for the Extended Affine Lie Algebra $\widetilde{\frak{gl}_l({\mathbb{C}_q})}$

利用自由域构造了广义仿射李代数$\widetilde{\frak{gl}_l({\bc_q})}$的一类模.给出了这类模不可约的一个充要条件。

On the hyperalgebra of the loop algebra ${\widehat{\frak{gl}}_n}$

Let $\widetilde{\mathcal U}_{\mathbb Z}({\widehat{\frak{gl}}_n})$ be the Garland integral form of ${\mathcal U}(\widehat{\frak{gl}}_n)$ introduced by Garland \cite{Ga}, where ${\mathcal U}(\widehat{\frak{gl}}_n)$ is the universal enveloping algebra of ${\widehat{\frak{gl}}_n}$. Using Ringel--Hall algebras, a certain integral form ${\mathcal U}_{\mathbb Z}(\widehat{\frak{gl}}_n)$ of ${\mathcal U}(\widehat{\frak{gl}}_n)$ was constructed in \cite{Fu13}. We prove that the Garland integral form $\widetilde{\mathcal U}_{\mathbb Z}({\widehat{\frak{gl}}_n})$ coincides with ${\mathcal U}_{\mathbb Z}(\w…

Highest weight Harish-Chandra supermodules and their geometric realizations. I. The infinitesimal theory

In this series of papers we want to discuss the highest weight ${\frak k}_r$-finite representations of the pair $({\frak g}_r,{\frak k}_r)$ consisting of ${\frak g}_r$, a real form of a complex basic Lie superalgebra of classical type ${\frak g}$ (${\frak g}\neq A(n,n)$), and the maximal compact subalgebra ${\frak k}_r$ of ${\frak} g_{r,0}$. These representations will be concretely realized through spaces of sections of holomorphic vector bundles on the associated Hermitian superspaces. In this part we shall discuss only the infinitesimal theory of the pair $({\frak g}_r, {\frak k}_r)$. We tre…

与李群$SO_0(2,m)$相关的III型紧局部埃尔米特对称空间中的特殊闭链

Special cycles in compact locally Hermitian symmetric spaces of type III associated with the Lie group $SO_0(2,m)$

本文针对李群$SO_0(2,m)$相关的III型紧局部埃尔米特对称空间，研究与嘉当对合交换的对合对应的特殊闭链，确定了其非零上同调类的存在性及对应上同调诱导表示的分量情况。

Borel-de Siebenthal 正根系

Borel-de Siebenthal Positive Root Systems

本文确定了简单李群的所有Borel-de Siebenthal正根系，并据此计算了非Hermitian对称情形下离散序列表示的酉等价类数目。