On the defining relations for generalized q-Schur algebras

TL;DR

This paper establishes a complete characterization of the defining relations for generalized q-Schur algebras, linking them to the ideal of a finite affine variety associated with weights, thereby unifying and extending prior results.

Contribution

It provides a comprehensive description of the relations for generalized q-Schur algebras based on the ideal of a finite affine variety, unifying previous findings.

Findings

Relations are determined by the ideal of a finite affine variety.

The approach unifies previous results on q-Schur algebras.

The characterization extends to a broader class of algebras.

Abstract

We show that the defining relations needed to describe a generalized q-Schur algebra as a quotient of a quantized enveloping algebra are determined completely by the defining ideal of a certain finite affine variety, the points of which correspond bijectively to the set of weights. This explains, unifies, and extends previous results.