TY  - BOOK
AU  - Deng,Bangming
AU  - Du,Jie
AU  - Fu,Qiang
TI  - A Double Hall Algebra Approach to Affine Quantum Schur–Weyl Theory
T2  - London Mathematical Society Lecture Note Series
SN  - 9781139226660 (ebook)
AV  - QA331.7  .D46 2012
U1  - 515.9 23
PY  - 2012///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Schur functions
KW  - Weyl groups
KW  - Representations of Lie groups
KW  - Affine algebraic groups
N1  - Title from publisher's bibliographic system (viewed on 16 Oct 2015)
N2  - 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
UR  - http://dx.doi.org/10.1017/CBO9781139226660
ER  -