THE INTEGRAL QUANTUM LOOP ALGEBRA OF gln
نویسندگان
چکیده
We will construct the Lusztig form for the quantum loop algebra of gln 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 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.
منابع مشابه
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The quantum loop algebra of gln is the affine analogue of quantum gln. In the seminal work [1], Beilinson–Lusztig–MacPherson gave a beautiful realisation for quantum gln via a geometric setting of quantum Schur algebras. Since then, generalising this work to the affine case and other cases (see, e.g., [9]) attracted much attention. For example, in [13, 21, 15, 20], affine quantum Schur algebras...
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