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arXiv · 1010.4619

A Double Hall Algebra Approach to Affine Quantum Schur--Weyl Theory

Bangming Deng·Jie Du·Qiang Fu
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Abstract

We investigate the structure of the double Ringel-Hall algebras associated with cyclic quivers and its connections with quantum loop algebras of $\mathfrak{gl}_n$, affine quantum Schur algebras and affine Hecke algebras. This includes their Drinfeld-Jimbo type presentation, affine quantum Schur-Weyl reciprocity, representations of affine quantum Schur algebras, and connections with various existing works by Lusztig, Varagnolo-Vasserot, Schiffmann, Hubery, Chari-Pressley, Frenkel-Mukhin, etc. We will also discuss conjectures on a realization of Beilinson-Lusztig-MacPherson type and Lusztig type integral forms for double Ringel-Hall algebras.

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BibTeXRIS

Bangming Deng, Jie Du, Qiang Fu. 2010-10-22. A Double Hall Algebra Approach to Affine Quantum Schur--Weyl Theory. https://arxiv.org/abs/1010.4619

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