The Integral quantum loop algebra of glₙ
Du, Jie · Fu, Qiang
Original · EN
We will construct the Lusztig form for the quantum loop algebra of glₙ by proving the conjecture [3.8.6]DDF 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 glₙ by introducing an affine stabilisation property and will lift the canonical bases from affine quantum Schur algebras to a canonical basis for this integral form. As an application of our theory, we will also discuss the integral form of the modified extended quantum affine slₙ and construct its canonical basis to verify a conjecture of Lusztig in this case.
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