Highest weight modules over quantum queer Lie superalgebra U_q(q(n))

TL;DR

This paper studies the structure and classification of highest weight modules over the quantum queer Lie superalgebra U_q(q(n)), establishing classical limit and reducibility results in a specific module category.

Contribution

It introduces a classification framework for finite dimensional irreducible modules over quantum Clifford superalgebras and proves key theorems for modules over U_q(q(n)).

Findings

Classical limit theorem for U_q(q(n))-modules.

Complete reducibility theorem in category O_q^{ extgreater=0}.

Triangular decomposition of U_q(q(n)).

Abstract

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for $U_q(q(n))$-modules in the category $O_q^{\geq 0}$.