The Integral Quantum Loop Algebra of $\mathfrak {gl}_{n}$
The Integral Quantum Loop Algebra of $\mathfrak {gl}_{n}$
Abstract We will construct the Lusztig form for the quantum loop algebra of $\mathfrak {gl}_{n}$ by proving the conjecture [4, 3.8.6] and establish partially the Schur–Weyl duality at the integral level in this case. We will also investigate the integral form of the modified quantum affine $\mathfrak {gl}_{n}$ by introducing …