Almost Gorenstein determinantal rings of symmetric matrices

TL;DR

This paper characterizes when determinantal rings of symmetric matrices are almost Gorenstein, providing explicit formulas for certain module ranks in their resolutions, advancing understanding of their algebraic structure.

Contribution

It offers a new characterization of almost Gorenstein determinantal rings of symmetric matrices and explicit formulas for module ranks in their resolutions.

Findings

Characterization of almost Gorenstein property for symmetric determinantal rings

Explicit formulas for ranks of modules in resolutions

Enhanced understanding of algebraic structure of these rings

Abstract

We provide a characterization of the almost Gorenstein property of determinantal rings of a symmetric matrix of indeterminates over an infinite field. We give an explicit formula for ranks of the last two modules in the resolution of determinantal rings using Schur functors.