TY - JOUR

T1 - Group actions on Stanley-Reisner rings and invariants of permutation groups

AU - Garsia, A. M.

AU - Stanton, D.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1984/2

Y1 - 1984/2

N2 - Let H be a group of permutations of x1,..., xn and let QH[x1, x2,..., xn] denote the ring of H-invariant Polynomials in x1, x2,..., xn with rational coefficients. Combinatorial methods for the explicit construction of free bases for QH[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 (Topology 14 (1975), 173-177) is obtained. Some applications to representation theory are also included.

AB - Let H be a group of permutations of x1,..., xn and let QH[x1, x2,..., xn] denote the ring of H-invariant Polynomials in x1, x2,..., xn with rational coefficients. Combinatorial methods for the explicit construction of free bases for QH[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 (Topology 14 (1975), 173-177) is obtained. Some applications to representation theory are also included.

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U2 - 10.1016/0001-8708(84)90005-7

DO - 10.1016/0001-8708(84)90005-7

M3 - Review article

AN - SCOPUS:0012858927

VL - 51

SP - 107

EP - 201

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -