对称积、线性表示和交换方案
Symmetric products, linear representations and the commuting scheme
摘要：
证明了交换环上的多对称函数环同构于交换一般矩阵中多项式的特征多项式的系数所生成的环。作为结果，我们给出了从多个矩阵的不变量环到多对称函数环的满射，推广了H.Weyl和F.Junker的一个经典结果。我们还发现了一个满射环的不变量的交换计划的环的多对称函数。这种满射是特征零域上的同构，并且在正特征的无限域上的约化结构的水平上诱导同构。
英文摘要：
We show that the ring of multisymmetric functions over a commutative ring is isomorphic to the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting generic matrices. As a consequence we give a surjection from the ring of invariants of several matrices to the ring of multisymmetric functions generalizing a classical result of H.Weyl and F.Junker. We also find a surjection from the ring of invariants over the commuting scheme to the ring of multisymmetric functions. This surjection is an isomophism over a characteristic zero field and induces an isomorphism at the level of reduced structures over an infinite field of positive characteristic.
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