# Finite dimensional irreducible representations of the nullity 2 centreless core $\mathfrak{g}_{2n,\rho}(\mathbb{C}_q)$

## TL;DR

This paper classifies finite-dimensional irreducible representations of a specific nullity 2 centreless core Lie algebra by analyzing its structure as a BC_n-graded Lie algebra over an involutory associative algebra.

## Contribution

It provides a detailed study of the structure and representation theory of the nullity 2 centreless core Lie algebra $rak{g}_{2n,
ho}(bC_q)$, extending understanding of its finite-dimensional irreducible modules.

## Key findings

- Classification of finite-dimensional irreducible representations.
- Structural insights into BC_n-graded Lie algebras.
- Connection between algebra structure and representation theory.

## Abstract

We study the finite-dimensional irreducible representations of the nullity 2 centreless core $\mathfrak{g}_{2n,\rho}(\mathbb{C}_q)$ by investigating the structure of the $\mathrm{BC}_n$-graded Lie algebra $\mathfrak{g}_{2n,\rho}(R)$, where $R$ is a unital involutory associative algebra over a field $k$ of characteristic zero.