论文标题
Witt Lie代数的多项式表示
Polynomial representations of the Witt Lie algebra
论文作者
论文摘要
witt代数w_n是N-变量多项式环V_n = C [X_1，...，...，X_N]的所有派生的代数（或A^n）的代数矢量字段。如果w_n表示为多项式，则作为v_n的张量幂之和的子量表。我们的主要定理断言W_N有限生成的多项式表示是Noetherian，并且具有理性的Hilbert系列。无限WITT代数的主要中间结果状态的多项式表示等同于Fin^op的表示，其中FIN是有限集的类别。我们还表明，w_n的多项式表示等同于a^n的内态的多项式表示。这些等价是我们确定的经营版本的schur-weyl二元性的特殊情况。
The Witt algebra W_n is the Lie algebra of all derivations of the n-variable polynomial ring V_n=C[x_1, ..., x_n] (or of algebraic vector fields on A^n). A representation of W_n is polynomial if it arises as a subquotient of a sum of tensor powers of V_n. Our main theorems assert that finitely generated polynomial representations of W_n are noetherian and have rational Hilbert series. A key intermediate result states polynomial representations of the infinite Witt algebra are equivalent to representations of Fin^op, where Fin is the category of finite sets. We also show that polynomial representations of W_n are equivalent to polynomial representations of the endomorphism monoid of A^n. These equivalences are a special case of an operadic version of Schur--Weyl duality, which we establish.
