b-Functions associated with quivers of type A

TL;DR

This paper investigates the b-functions of relative invariants linked to type A quivers, providing explicit formulas and a graphical algorithm for multi-variable cases, advancing understanding of their algebraic properties.

Contribution

It introduces a graphical algorithm and explicit formulas for b-functions of invariants associated with type A quivers, enhancing computational methods in this area.

Findings

Explicit formulas for one-variable b-functions for each invariant

A graphical algorithm for multi-variable b-functions

Improved computational approach for invariants of type A quivers

Abstract

We study the b-functions of relative invariants of the prehomogeneous vector spaces associated with quivers of type A. By applying the decomposition formula for b-functions, we determine explicitly the b-functions of one variable for each irreducible relative invariant. Moreover, we give a graphical algorithm to determine the b-functions of several variables.