基本多项式不变量、基本表示和Chern class映射
Basic polynomial invariants, fundamental representations and the Chern class map
摘要：
考虑一个晶体学根系及其Weyl群$W$作用在权格$M$上。设$Z[M]^W$和$S^*(M)^W$分别是整群环$Z[M]$和对称代数$S^*(M)$的$W$不变子环. Chevalley的一个著名定理说，$Z[M]^W$是在基本表示类$w_1,...,w_n$中的$Z$上的多项式环，而有理数上的$S^*(M)^{W}$是在基本多项式不变量$q_1,...,q_n$中的多项式环，其中$n$是秩。本文建立并研究了整数上的$w_i$与$q_i$之间的关系。作为应用，我们给出了相应线性代数群的Borel子群簇上的Grothendieck γ-滤子的第3和第4阶导数的挠部分的零化子.
英文摘要：
Consider a crystallographic root system together with its Weyl group $W$ acting on the weight lattice $M$. Let $Z[M]^W$ and $S^*(M)^W$ be the $W$-invariant subrings of the integral group ring $Z[M]$ and the symmetric algebra $S^*(M)$ respectively. A celebrated theorem of Chevalley says that $Z[M]^W$ is a polynomial ring over $Z$ in classes of fundamental representations $w_1,...,w_n$ and $S^*(M)^{W}$ over rational numbers is a polynomial ring in basic polynomial invariants $q_1,...,q_n$, where $n$ is the rank. In the present paper we establish and investigate the relationship between $w_i$'s and $q_i$'s over the integers. As an application we provide an annihilator of the torsion part of the 3rd and the 4th quotients of the Grothendieck gamma-filtration on the variety of Borel subgroups of the associated linear algebraic group.
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