Abstract We describe a linear equivariant isomorphism from the enveloping algebra to the algebra of polynomials in the entries of a “generic” square matrix of order n. The isomorphism maps any Capelli bitableau in to the (determinantal) bitableau in and any Capelli *-bitableau in to the (permanental) *-bitableau in These results are far-reaching generalizations of the pioneering result of Koszul on the Capelli determinant in We introduce column Capelli bitableaux and *-bitableaux in Section 6; since they are mapped by the isomorphism to monomials in this isomorphism can be regarded as a sharpened version of the PBW isomorphism for the enveloping algebra Since the center of equals the subalgebra of invariants then

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关于 Koszul 映射对一般线性李代数的包络代数的作用

摘要 我们描述了从包络代数到多项式代数的线性等变同构，在 n 阶“通用”方阵的条目中。同构将任何 Capelli bitableau in 映射到（行列式）bitableau in 和任何 Capelli *-bitableau in 到（永久）*-bitableau in 这些结果是 Koszul 在 Capelli 行列式中的开创性结果的深远概括我们介绍第 6 节中的 Capelli bitableaux 和 *-bitableaux 列；因为它们在这个同构中被同构映射到单项式可以被看作是包络代数的 PBW 同构的一个锐化版本 因为等于的中心是不变量的子代数那么