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arXiv · 1404.5679

The Integral quantum loop algebra of $\mathfrak{gl}_n$

Jie Du·Qiang Fu
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Abstract

We will construct the Lusztig form for the quantum loop algebra of $\mathfrak{gl}_n$ by proving the conjecture \cite[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 $\mathfrak{gl}_n$ 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 $\mathfrak{sl}_n$ and construct its canonical basis to verify a conjecture of Lusztig in this case.

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BibTeXRIS

Jie Du, Qiang Fu. 2014-04-23. The Integral quantum loop algebra of $\mathfrak{gl}_n$. https://arxiv.org/abs/1404.5679

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