Let T < GL_(n,K) be the Borel group of upper triangular matrices. In this paper we want to study the action of T on the set of monomial ideals of K[x_1,...,x_n] (K a field of characteristic zero) from a computational point of view. More specifically, we show that the stabilizer of a monomial ideal M < K[x_1,...,x_n] in T is a purely combinatorial object and we give an algorithm for computing it. Then we characterize the subgroups of T that are stabilizers of monomial ideals, we give an algorithm which finds if a given ideal J is in the orbit of a monomial ideal M under the action of T and in the affirmative case, finds the matrices W in T such that W * J = M. We show that the entries of W can be directly obtained from the coefficients of the generators of J, so in particular no solutions of polynomial equations are required.

Action of the Borel group on monomial ideals

LA SCALA, Roberto;
2002-01-01

Abstract

Let T < GL_(n,K) be the Borel group of upper triangular matrices. In this paper we want to study the action of T on the set of monomial ideals of K[x_1,...,x_n] (K a field of characteristic zero) from a computational point of view. More specifically, we show that the stabilizer of a monomial ideal M < K[x_1,...,x_n] in T is a purely combinatorial object and we give an algorithm for computing it. Then we characterize the subgroups of T that are stabilizers of monomial ideals, we give an algorithm which finds if a given ideal J is in the orbit of a monomial ideal M under the action of T and in the affirmative case, finds the matrices W in T such that W * J = M. We show that the entries of W can be directly obtained from the coefficients of the generators of J, so in particular no solutions of polynomial equations are required.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/3389
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