Download PDF by Bangming Deng,Jie Du,Qiang Fu: A Double Hall Algebra Approach to Affine Quantum Schur-Weyl

By Bangming Deng,Jie Du,Qiang Fu

the idea of Schur–Weyl duality has had a profound impact over many components of algebra and combinatorics. this article is unique in respects: it discusses affine q-Schur algebras and provides an algebraic, in place of geometric, method of affine quantum Schur–Weyl thought. to start, a variety of algebraic buildings are mentioned, together with double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. the remainder of the booklet investigates the affine quantum Schur–Weyl duality on 3 degrees. This comprises the affine quantum Schur–Weyl reciprocity, the bridging position of affine q-Schur algebras among representations of the quantum loop algebras and people of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with an evidence of the classical case. this article is perfect for researchers in algebra and graduate scholars who are looking to grasp Ringel–Hall algebras and Schur–Weyl duality.

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A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory (London Mathematical Society Lecture Note Series) by Bangming Deng,Jie Du,Qiang Fu

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