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

Groupes et algébres de lie

Introduction to lie algebras and representation theory

By Vyjayanthi Chari and Andrew Pressley: 651 pp., £22.95 (US$34.95), isbn 0 521 55884 0 (Cambridge University Press, 1994).

A guide to quantum groups

We construct a 2-category associated with a Kac-Moody algebra and we study its 2-representations. This generalizes earlier work with Chuang for type A. We relate categorifications relying on K_0 properties and 2-representations.

2-Kac-Moody algebras

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki’s categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial ℤ-grading on blocks of cyclotomic Hecke algebras, including symmetric groups in positive characteristic.

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Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Preface Part I. Linear Representations: 1. Notion and generalities 2. Symmetric groups I 3. Degenerate affine Hecke algebra 4. First results on Hn modules 5. Crystal operators 6. Character calculations 7. Integral representations and cyclotomic Hecke algebras 8. Functors e and f 9. Construction of Uz and irreducible modules 10. Identification of the crystal 11. Symmetric groups II Part II. Projective Representations: 12. Generalities on superalgebra 13. Sergeev superalgebras 14. Affine Sergeev superalgebras 15. Integral representations and cyclotomic Sergeev algebras 16. First results on Xn modules 17. Crystal operators fro Xn 18. Character calculations for Xn 19. Operators e and f 20. Construction of Uz and irreducible modules 21. Identification of the crystal 22. Double covers References Index.

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Linear and Projective Representations of Symmetric Groups

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki's categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial Z-grading on blocks of cyclotomic Hecke algebras, including symmetric groups in positive characteristic.

https://pages.uoregon.edu/brundan/papers/lltfinal.pdf

Alexander Kleshchev

Papers

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Linear and Projective Representations of Symmetric Groups

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

Graded decomposition numbers for cyclotomic Hecke algebras

Branching Rules for Modular Representations of Symmetric Groups III: Some Corollaries and a Problem of Mullineux