I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions with two parameters VII. Zonal polynomials

Symmetric functions and Hall polynomials

1. Symmetric groups and their young subgroups 2. Ordinary irreducible representations and characters of symmetric and alternating groups 3. Ordinary irreducible matrix representations of symmetric groups 4. Representations of wreath products 5. Applications to combinatories and representation theory 6. Modular representations 7. Representation theory of Sn over an arbitrary field 8. Representations of general linear groups Appendices Index.

The representation theory of the symmetric group

Group representations in probability and statistics

Quantum theory: Concepts and methods

Polynomial Representations of GLn(K): The Schur algebra.- Weights and Characters.- The modules D?,K.- The Carter-Lusztig modules V?,K.- Representation theory of the symmetric group.

Polynomial representations of GLn

Background from representation theory.- The symmetric group.- Diagrams, tableaux and tabloids.- Specht modules.- Examples.- The character table of .- The garnir relations.- The standard basis of the specht module.- The branching theorem.- p-regular partitions.- The irreducible representations of .- Composition factors.- Semistandard homomorphisms.- Young's rule.- Sequences.- The Littlewood-richardson rule.- A specht series for M?.- Hooks and skew-hooks.- The determinantal form.- The hook formula for dimensions.- The murnaghan-nakayama rule.- Binomial coefficients.- Some irreducible specht modules.- On the decomposition matrices of .- Young's orthogonal form.- Representations of the general linear group.

The Representation Theory of the Symmetric Groups

Representations of Hecke Algebras of General Linear Groups

This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

/pdf/representations-and-characters-of-groups-oy3rgftl0x.pdf

Gordon James

Papers

The representation theory of the symmetric group

The Representation Theory of the Symmetric Groups

Representations of Hecke Algebras of General Linear Groups

Representations and Characters of Groups

Cyclotomic q –Schur algebras