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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...

The interplay between finite dimensional algebras and Lie theory dates back many years. This book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the represenation theory of quivers with automorphisms and much more.