A Double Hall Algebra Approach to Affine Quantum Schur--Weyl Theory
Quantum Algebra
2010-10-25 v1 Rings and Algebras
Representation Theory
Abstract
We investigate the structure of the double Ringel-Hall algebras associated with cyclic quivers and its connections with quantum loop algebras of , 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.
Keywords
Cite
@article{arxiv.1010.4619,
title = {A Double Hall Algebra Approach to Affine Quantum Schur--Weyl Theory},
author = {Bangming Deng and Jie Du and Qiang Fu},
journal= {arXiv preprint arXiv:1010.4619},
year = {2010}
}
Comments
166 pages