辛理想与双中心化定理
The symplectic ideal and a double centraliser theorem
摘要：
我们解释了S. Oehms作为关于辛理想的陈述。利用这个结果证明了辛群作用在\bigoplus_{r=0}^s \otimes^r V上的一个双中心化定理，其中V是辛群的自然模.这个结果是H.外尔利用这一点，我们将作者的一个结果推广到任意连通的具有单连通导群的约化群G上，即G上的正则函数代数中的无穷小不变量代数K[G]^g是唯一的因子分解整环.
英文摘要：
We interpret a result of S. Oehms as a statement about the symplectic ideal. We use this result to prove a double centraliser theorem for the symplectic group acting on \bigoplus_{r=0}^s\otimes^rV, where V is the natural module for the symplectic group. This result was obtained in characteristic zero by H. Weyl. Furthermore we use this to extend to arbitrary connected reductive groups G with simply connected derived group the earlier result of the author that the algebra K[G]^g of infinitesimal invariants in the algebra of regular functions on G is a unique factorisation domain.
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