Sub-bimodules of the identity bimodule for cyclic quivers

TL;DR

This paper explores the combinatorial structure of sub-bimodules within the tensor category of the identity bimodule for cyclic quivers with various orientations, providing a detailed mathematical framework.

Contribution

It introduces a comprehensive combinatorial description of the multisemigroup with multiplicities for sub-bimodules in cyclic quivers, extending previous understanding.

Findings

Provides a combinatorial model for sub-bimodules

Describes the multisemigroup structure explicitly

Applies to arbitrary non-uniform orientations

Abstract

We describe the combinatorics of the multisemigroup with multiplicities for the tensor category of subbimodules of the identity bimodule, for an arbitrary non-uniform orientation of a finite cyclic quiver.