The theory of Schur-Weyl 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
Schur-Weyl theory. To begin, various algebraic structures are
discussed, including double Ringel-Hall algebras of cyclic quivers
and their quantum loop algebra interpretation. The rest of the book
investigates the affine quantum Schur-Weyl duality on three levels.
This includes the affine quantum Schur-Weyl 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 Ringel-Hall algebra with
a proof of the classical case. This text is ideal for researchers
in algebra and graduate students who want to master Ringel-Hall
algebras and Schur-Weyl duality.
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