Group actions on Stanley-Reisner rings and invariants of permutation groups☆
Group actions on Stanley-Reisner rings and invariants of permutation groups☆
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DOI：
10.1016/0001-8708(84)90005-7
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发表时间：
1984-02
影响因子：
1.7
通讯作者：
A. Garsia;D. Stanton
中科院分区：
文献类型：
--
作者：
A. Garsia;D. Stanton
设为x1，…的一组排列，xn和letQh[x1，x2，…，xn]表示由x1，x2，…中的h不变多项式组成的环，Xn具有有理系数。显式构造QH[x1，x2，…]自由基的组合方法，xn]作为对称多项式上的模。这些方法是通过研究对称群在子集格的Stanley-Reisner环上的作用而发展起来的。通过研究Coxeter群在相应Coxeter复形的Stanley-Reisner环上的作用，得到了一些一般性的结果。对于Weyl群，得到了由R.Steinberg(Topology 14(1975)，173-177)首先考虑的某些不变量的纯组合构造。文中还介绍了表象理论的一些应用。
LetHbe a group of permutations ofx1,…,xnand letQH[x1,x2,…,xn] denote the ring ofH-invariant Polynomials inx1,x2,…,xnwith rational coefficients. Combinatorial methods for the explicit construction of free bases forQH[x1,x2,…,xn] as a module over the symmetric polynomials are developed. The methods are developed by studying the action of the symmetric group on the Stanley-Reisner ring of the subset lattice. Some general results are also obtained by studying the action of a Coxeter group on the Stanley-Reisner ring of the corresponding Coxeter complex. In the case of a Weyl group, a purely combinatorial construction of certain invariants first considered by R. Steinberg (Topology14(1975), 173–177) is obtained. Some applications to representation theory are also included.