Tensor product algebras in type A are Koszul

TL;DR

This paper proves that certain tensor product algebras in type A are Koszul by establishing a graded Morita equivalence with blocks of category O, enhancing understanding of their algebraic structure.

Contribution

The paper introduces a proof of Koszulity for tensor product algebras in type A using graded Morita equivalence with category O blocks, providing new insights into their structure.

Findings

Tensor product algebra in type A is Koszul.

Constructs a graded Morita equivalence with category O.

Enhances understanding of algebraic and categorical structures.

Abstract

In this note, we prove the Koszulity of the tensor product algebra defined in the author's previous work for sl(n) and a list of fundamental weights. This is achieved by constructing a graded Morita equivalence between the modules over this algebra and a sum of blocks of category O in type A.