Combinatorics of Fourier transforms for type A quiver representations

TL;DR

This paper introduces two novel combinatorial algorithms using triangular arrays to compute Fourier transforms of simple perverse sheaves on type A quiver representation moduli spaces, simplifying orbit descriptions.

Contribution

It presents new combinatorial algorithms for Fourier transforms on quiver representations and offers concise descriptions of orbit closures and dimensions.

Findings

Algorithms effectively compute Fourier transforms.

Concise descriptions of orbit closure partial order.

Simplified dimension calculations for orbits.

Abstract

We describe two new combinatorial algorithms (using the language of "triangular arrays") for computing the Fourier transforms of simple perverse sheaves on the moduli space of representations of an equioriented quiver of type A. (A rather different solution to this problem was previously obtained by Knight-Zelevinsky.) Along the way, we also show that the closure partial order and the dimensions of orbits have especially concise descriptions in the language of triangular arrays.