Cellularity and subdivision of KLR and weighted KLRW algebras

TL;DR

This paper develops cellular bases for weighted KLRW algebras and their cyclotomic quotients, providing new insights into their structure and relations between different types, especially in affine types A and C.

Contribution

It constructs homogeneous affine cellular bases for weighted KLRW algebras in affine types A and C, and introduces subdivision homomorphisms linking these algebras for different quivers.

Findings

Cellular bases for affine type A and C weighted KLRW algebras.

Subdivision homomorphisms relating different weighted KLRW algebras.

Reproof that cyclotomic KLR algebras of affine types are graded cellular.

Abstract

Weighted KLRW algebras are diagram algebras generalizing KLR algebras. This paper undertakes a systematic study of these algebras culminating in the construction of homogeneous affine cellular bases in affine types A and C, which immediately gives cellular bases for the cyclotomic quotients of these algebras. In addition, we construct subdivision homomorphisms that relate weighted KLRW algebras for different quivers. As an application we obtain new results about the (cyclotomic) KLR algebras of affine type, including (re)proving that the cyclotomic KLR algebras of type A^{(1)}_{e} and C^{(1)}_{e} are graded cellular algebras.