Jordan-H\"older decomposition of regular $(a, b)$-modules

TL;DR

This paper proves a symmetry property of the Jordan-H"older composition series of $(a,b)$-modules linked to isolated hypersurface singularities, extending classical spectral symmetry results.

Contribution

It establishes a new symmetry result for the Jordan-H"older series of $(a,b)$-modules in singularity theory, paralleling classical spectral symmetry.

Findings

Symmetry in the Jordan-H"older series of $(a,b)$-modules

Extension of classical spectral symmetry to algebraic modules

New insights into hypersurface singularity invariants

Abstract

A classical result of singularity theory states that the spectrum of an isolated hypersurface singularity is symmetric with respect to $n/2$, where $n$ is the dimension of the enclosing space. We prove a similar result for the Jordan-H\"older composition series of the $(a,b)$-module associated to an isolated hypersurface singularity.