Work

A -basis of the -invariant Subring of

Year: 2025

Type: article

Abstract: Let be the subring of the polynomial ring of independent variables generated by the differences . Let be the invariant subring of under the action of the symmetric group of degree defined by . We investigate and construct a -basis of the submodules of of degree under certain conditions. Furthermore, is expressed as the kernel of the differential operator of the -invariant subring for elementary symmetric polynomials of degree of . With respect to an ordered -basis of , we determine the exponents on the minimal terms of the -basis vectors of (Theorem A).

Source: JP Journal of Algebra Number Theory and Applications

DOI: 10.17654/0972555525015

Author: Takashi Maeda

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4408998178

FWCI:

Cites:

Cited by:

Related to: 10