دانلود کتاب Three Lectures in Algebra

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Table of Contents
Foreword
Special Functions over Finite Fields by MASAO KOIKE
Introduction
1. Functions over finite field
2. Finite analogue of binomial and trinomial coefficients
3. Hypergeometric series over finite fields
4. Hypergeometric polynomials over finite fields
5. Applications
5.1 Congruences of Apery numbers
5.2 Linear factors of hypergeometric polynomials
5.3 Cubic and quartic transformation identities
5.4 Honda\'s result
References
Complex Reflection Groups and Cyclotomic Hecke Algebras by Toshiaki SHOJI
Introduction
1. Coxeter groups and complex reflection groups
1.1. Finite reflection groups
1.2. Coxeter groups
1.3. Root systems of Coxeter groups
1.4. Examples of root systems
1.5. The length function
1.6. Complex reflection groups
2. Length functions of complex reflection groups
2.1. A presentation for G(r,1,n)
2.2. A root system for G(r,1,n)
2.3. A length function associated to Φ
2.4. A normal form for elements in G(r,1,n)
2.5. A characterization of the function n(w)
2.6. A length function for G(r,r,n)
3. Demazure operators
3.1. Demazure operators for Coxeter groups
3.2. Demazure operators for complex reflection groups
4. Cyclotomic Hecke algebras
4.1. Hecke algebras of Coxeter groups
4.2. Cyclotomic Hecke algebras
5. Schur-Weyl reciprocity
5.1. Schur-Weyl reciprocity for the symmetric groups
5.2. Schur-Weyl reciprocity for complex reflection groups
5.3. Schur-Weyl reciprocity for Hecke algebras
5.4. Schur-Weyl reciprocity for cyclotomic Hecke algebras
5.5. Semisimplicity of H_{n,r}
References
An Introduction to Distance-Regular Graphs by Hiroshi SUZUKI
Contents
Chapter 1. Introduction
1.1 Distance-Transitive and Distance-Regular Graphs
1.2 Basic Properties
1.3 Intersection Diagrams
1.4 A. A. lvanov\'s Bound
1.5 Absolute Constant Bound Conjecture
1.6 Examples
Chapter 2. Algebraic Methods
2.1 Adjacency Matrices of Distance-Regular Graphs
2.2 Association Schemes
2.3 Primitive Idempotents and Eigen Matrices
2.4 Multiplicity Formulas
2.5 Q-polynomial Properties and Other Related Structures
2.6 Eigenvalue Techniques
Chapter 3. Combinatorial Methods
3.1 Incidence Graphs
3.1.1 Distance-Regular Graphs of Order (s, t) and Their Incidence Graphs
3.1.2 Distance-Regular Graphs of Order (s, t) with small t
3.1.3 Regularities of Incidence Graphs
3.2 Subgraph Theorems
3.2.1 Types of Strongly Closed Subgraphs
3.2.2 Existence Conditions
3.2.3 Pararnetrical Conditions
Appendix A. Supplements
A.1 Interlacing of Eigenvalues
A.2 Thin Graphs
A.2.1 Introduction
A.2.2 Terwilliger Algebra of a Graph
A.2.3 Trivial Module
A.2.4 The Bound of the Girth
Appendix B. Examples
B.1 Definitions
B.2 Examples
Primitive distance-regular graph with d >= 4, k >= 3
Primitive Sporadic distance-regular graphs with d >= 4
Bibliography