Seminar Bielefeld 1997/98 : Hall Algebras

Part 1 : Macdonald, Symmetric functions and Hall polynomials

1. Steffen König, Introduction
2. Jan Schröer, LR-Sequences
3. Pham Ngoc Anh, Hall polynomials
4. Dietmar Guhe, Hall-Littlewood polynomials
5. Thomas Brüstle, Symmetric functions and Hall algebras
6. Gerhard Röhrle, Symmetric functions and general linear groups - a survey
7. Gerhard Röhrle, The characters of GL_n(q); the characteristic map
8. Steffen König, Construction of the characters of GL_n(q)
9. Gerhard Röhrle, Examples of character tables of GL_n(q), Hall polynomials and Green polynomials
10. Thomas Brüstle, Hopf algebras and the characters of GL_n(q)

Part 2 : Ringel-Hall algebras

1. Rainer Nörenberg, Hall algebras for finitary rings I
2. Steffen König, Hall algebras for finitary rings II
3. Pham Ngoc Anh, Loewy series and the fundamental relations in the Hall algebra
4. Bangming Deng, twisted Hall algebras
5. Jan Schröer, twisted Hall algebra of a Dynkin quiver and the positive part of a quantum group
6. Dietmar Guhe, examples of canonical bases, in particular the cases A_2 and A_3
7. Steffen König, survey on canonical bases
8. Claus Ringel, Hall polynomials

Part 3 : Green's theorem

1. Thomas Brüstle, Green's formula
2. Bangming Deng, The bialgebra structure.
3. Thomas Brüstle, Generic composition algebras, Quantum Serre relations
4. Steffen König, Quantized shuffles
5. Steffen König, Composition algebras and quantum groups

Part 4 : Quantum groups

1. Peter Dräxler, On the coloured graph structure of Lusztigs canonical basis (on work of Reineke)
2. Peter Dräxler, On the coloured graph structure of Lusztigs canonical basis II
3. Markus Reineke, Generic extensions and Hall algebras at q=0