Quiver relations and associated symmetric polynomials

TL;DR

This paper explores the connection between quiver relations and symmetric polynomials by constructing a morphism that embeds quiver grassmannians into symmetric function spaces.

Contribution

It introduces a method to solve quiver relations to identify path algebra elements with symmetric functions, advancing the understanding of quiver grassmannians.

Findings

Established a morphism linking quiver relations to symmetric functions

Solved quiver relations for specific embeddings

Enhanced the algebraic understanding of quiver grassmannians

Abstract

The idea is to identify certain path algebra elements with symmetric functions. We propose such a morphism by solving the quiver relations, which describe the Plucker-type embedding for quiver grassmannians.