D_n型泛包络代数的中心元
A central element in the universal enveloping algebra of type D_n via minor summation formula of Pfaffians
摘要：
已知大小为偶数的正交李代数的泛包络代数有一个中心元表示为沿反对角线交错（简称反交错）的矩阵的Pfalan，其元素在泛包络代数中.本文建立了非交换反交错矩阵和交换反交错矩阵的Pfalan小求和公式。作为一个应用，我们证明了Pfidian给出的中心元的最高权模上的特征值可以很容易地计算。
英文摘要：
It is known that the universal enveloping algebra of the orthogonal Lie algebra of size even has a central element expressed in terms of Pfaffian of a certain matrix alternating along the anti-diagonal (which we call anti-alternating for short) whose entries are in the univerasal enveloping algebra. In this paper, we establish minor summation formulae of Pfaffian for the noncommutative anti-alternating matrix, as well as for commutative anti-alternating matrix. As an application, we show that the eigenvalues on the highest weight modules of the central element given by the Pfaffian can be easily computed.
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