Representations of quantum orders

TL;DR

This paper investigates the structure of quantum orders by analyzing finite dimensional algebras as fibers over points in the center's variety, providing formulas for counting irreducible representations and validating them on specific quantum algebras.

Contribution

It introduces a formula for the number of irreducible representations of quantum order fibers and verifies it on several key quantum algebras.

Findings

Derived a formula for counting irreducible representations.

Validated the formula on twisted polynomial algebra, quantum Weyl algebra, and quantum group functions.

Enhanced understanding of the structure of quantum orders and their representations.

Abstract

We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted polynomials, the quantum Weyl algebra and the algebra of regular functions on quantum group.