A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory (London Mathematical Society Lecture Note Series) Qiang Fu » holypet.ru

Schur-Weyl 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 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. Oct 22, 2010 · Abstract: We investigate the structure of the double Ringel-Hall algebras associated with cyclic quivers and its connections with quantum loop algebras of $\mathfrakgl_n$, affine quantum Schur algebras and affine Hecke algebras. This includes their Drinfeld-Jimbo type presentation, affine quantum Schur-Weyl reciprocity, representations of affine quantum Schur algebras, and. A Double Hall Algebra Approach to Affine Quantum Schur--Weyl Theory. Qiang Fu. 16.48; Tongji University. affine quantum Schur-Weyl reciprocity, representations of affine quantum Schur.

arXiv:1010.4619v1 [math.QA] 22 Oct 2010 A Double Hall Algebra Approach to Affine Quantum Schur–Weyl Theory BangmingDeng JieDu QiangFu† School of Mathematical Sciences,Beijing. [DDF] Bangming Deng, Jie Du, and Qiang Fu, A double Hall algebra approach to affine quantum Schur-Weyl theory, London Mathematical Society Lecture Note Series, vol. 401, Cambridge University Press, Cambridge, 2012. MR 3113018 [GL] J. J. Graham and G. I. Lehrer, Cellular algebras, Invent. Math. 123 1996, no. 1, 1–34. Finite dimensional irreducible modules for the affine quantum Schur algebra SΔn,rt were classified in [B. Deng, J. Du and Q. Fu, A Double Hall Algebra Approach to Affine Quantum Schur-Weyl. In 1990, Beilinson–Lusztig–MacPherson BLM discovered a realization for quantum 픤픩n via a geometric setting of quantum Schur algebras. We will generalize their result to the classical affine.

3.2. Schur-Weyl Duality for GLV 15 3.3. Schur Functors and Algebraic Representations 16 3.4. Other Cases of Schur-Weyl Duality 17 Appendix A. Semisimple Algebras and Double Centralizer Theorem 19 Acknowledgments 20 References 21 Introduction. In this paper, we build up to one of the remarkable results in representation theory called Schur. Schur-Weyl 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. 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.

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