By Bangming Deng
The speculation of Schur-Weyl duality has had a profound impression over many parts of algebra and combinatorics. this article is unique in respects: it discusses affine q-Schur algebras and offers an algebraic, instead of geometric, method of affine quantum Schur-Weyl idea. to start, quite a few algebraic buildings are mentioned, together with double Ringel-Hall algebras of cyclic quivers and their quantum loop algebra interpretation. the remainder of the ebook 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 explanation 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.
Read or Download A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory (London Mathematical Society Lecture Note Series) PDF
Best Algebra Trigonometry books
Thought of sheaves.
Linear algebra and matrix idea are primarily synonymous phrases for a space of arithmetic that has develop into some of the most beneficial and pervasive instruments in quite a lot of disciplines. it's also a subject matter of serious mathematical attractiveness. consequently of either one of those evidence, linear algebra has more and more been introduced into decrease degrees of the curriculum, both along side the calculus or become independent from it yet on the related point.
Beecher, Penna, and Bittinger’s Algebra and Trigonometry is understood for allowing scholars to “see the mathematics” via its specialize in visualization and early creation to capabilities. With the Fourth version, the authors proceed to innovate through incorporating extra ongoing evaluate to assist scholars improve their figuring out and examine successfully.
Extra resources for A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory (London Mathematical Society Lecture Note Series)
- Download E-books Lectures on Real Semisimple Lie Algebras and Their Representations (ESI Lectures in Mathematics & Physics) PDF
- Download E-books Theory of Sheaves PDF