Quantized Algebra and Physics: Proceedings of International Workshop, Tianjin, China, 23-26 July 2009

The book aims to survey recent developments in quantum algebras and related topics. Quantum groups were introduced by Drinfeld and Jimbo in 1985 in their work on Yang-Baxter equations. The subject from the very beginning has been an interesting one for both mathematics and theoretical physics. For example, Yangian is a special example of quantum group, corresponding to rational solution of Yang-Baxter equation. Viewed as a generalization of the symmetric group, Yangians also have close connections to algebraic combinatorics. This is the proceeding for the International Workshop on Quantized Algebra and Physics. The workshop aims to gather experts and young investigators from China and abroad to discuss research problems in integrable systems, conformal field theory, string theory, Lie theory, quantum groups including Yangians and their representations.

Sample Chapter(s)
Chapter 1: A Note on Brauer-Schur Functions (417 KB)
Contents: A Note on Brauer-Schur Functions "(Kazuya Aokage, Hiroshi Mizukawa and Hiro-Fumi Yamada)"$\mathcal O$-Operators on Associative Algebras, Associative Yang-Baxter Equations and Dendriform Algebras "(Chengming Bai, Li Guo and Xiang Ni)"Irreducible Wakimoto-like Modules for the Affine Lie Algebra $\widehat{\mathfrak gl_n}$ "(Yun Gao and Ziting Zeng)"Verma Modules Over Generic Exp-Polynomial Lie Algebras "(Xiangqian Guo, Xuewen Liu and Kaiming Zhao)"A Formal Infinite Dimensional Cauchy Problem and its Relation to Integrable Hierarchies "(G F Helminck, E A Panasenko and A O Sergeeva)"Partially Harmonic Tensors and Quantized Schur-Weyl Duality "(Jun Hu and Zhankui Xiao)"Quantum Entanglement and Approximation by Positive Matrices "(Xiaofen Huang and Naihuan Jing)"2-Partitions of Root Systems "(Bin Li, William Wong and Hechun Zhang)"A Survey on Weak Hopf Algebras "(Fang Li and Qinxiu Sun)"The Equitable Presentation for the Quantum Algebra "Uq"("f"("k")) "(Yan Pan, Meiling Zhu and Libin Li)"
Readership: Graduate students in mathematics and theoretical physics; mathematicians and mathematical physicists.