On the quantum superalgebra U_q(gl(m,n)) and its representations at roots of 1

TL;DR

This paper provides an algebraic proof of the PBW theorem for the quantum superalgebra U_q(gl(m,n)), extends Lusztig's conjecture to the super case, and proves the tensor product theorem.

Contribution

It introduces a purely algebraic proof of the PBW theorem for U_q(gl(m,n)) and extends key Lusztig conjectures to the superalgebra context.

Findings

Algebraic proof of PBW theorem for U_q(gl(m,n))

Extension of Lusztig's conjecture to superalgebras

Establishment of Lusztig's tensor product theorem in the super case

Abstract

An purely algebraic proof of the PBW theorem of U_q(gl(m,n)) is given. Lusztig's conjecture is extended to the super case. The Lusztig's tensor product theorem is established.