Symmetric Complete Intersections

TL;DR

This paper studies symmetric complete intersection ideals in polynomial rings, classifying their representation types and providing formulas for the graded characters of their quotient rings, advancing understanding of symmetry in algebraic structures.

Contribution

It characterizes the representation types of symmetric complete intersection ideals and derives explicit formulas for the graded characters of their quotient rings.

Findings

Classification of possible representation types.

Formulas for graded characters of quotient rings.

Insights into symmetry in algebraic structures.

Abstract

We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these ideals, and describe formulas for the graded characters of the corresponding quotient rings.