A Double Hall Algebra Approach to Affine Quantum Schur}}}Weyl Theory [Paperback]

The first book of its kind to present an algebraic approach to affine q-Schur algebras and affine quantum SchurWeyl theory.SchurWeyl duality has had a profound influence over many areas of mathematics. This text is original in presenting an algebraic approach to the theory in the quantum affine case. Three levels of duality are investigated making this text ideal for researchers and graduate students who wish to master the theory.SchurWeyl duality has had a profound influence over many areas of mathematics. This text is original in presenting an algebraic approach to the theory in the quantum affine case. Three levels of duality are investigated making this text ideal for researchers and graduate students who wish to master the theory.The theory of SchurWeyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum SchurWeyl theory. To begin, various algebraic structures are discussed, including double RingelHall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum SchurWeyl duality on three levels. This includes the affine quantum SchurWeyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double RingelHall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master RingelHall algebras and SchurWeyl duality.Introduction; 1. Preliminaries; 2. Double RingelHall algebras of cyclic quivers; 3. Affine quantum Schur algebras and the SchurWeyl reciprocity; 4. Representations of affine quantum Schur algebras; 5. The presentation and realization lº