# Representation Theory

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*Zongzhu Lin; Jianpan Wang*

Articles in this volume cover topics related to representation theory of various algebraic objects such as algebraic groups, quantum groups, Lie algebras, (finite- and infinite-dimensional) finite groups, and quivers. Collected in one book, these articles show deep relations between all these aspects of Representation Theory, as well as the diversity of algebraic, geometric, topological, and categorical techniques used in studying representations.

#### Readership

Graduate students and research mathematicians interested in representation theory.

# Table of Contents

## Representation Theory

- Contents v7 free
- Preface vii9 free
- List of Talks ix11 free
- List of Participants xiii15 free
- Sum formulas and Ext-groups 119 free
- Schur-Weyl duality in positive characteristic 1533
- The centers of Iwahori-Hecke algebras are filtered 2947
- On Kostant's theorem for Lie algebra cohomology 3957
- G-stable pieces and partial flag varieties 6179
- Steinberg representations and duality properties of arithmetic groups, mapping class groups, and outer automorphism groups of free groups 7189
- 1. Introduction 7290
- 2. Poincaré duality of closed manifolds and generalizations 7492
- 3. Homology and cohomology of groups 7694
- 4. Duality groups, Poincaré duality groups 7896
- 5. Algebraic groups, Tits building, Steinberg representations, arithmetic subgroups 8199
- 6. Borel-Serre compactification and duality properties of arithmetic subgroups 83101
- 7. Mapping class groups and Teichmüller spaces 89107
- 8. Curve complex, duality properties of mapping class groups 90108
- 9. Outer automorphism groups of free groups, outer space 92110
- 10. Duality properties of outer automorphism groups 94112
- 11. Comments and conjectures 95113
- References 97115

- Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups 99117
- Classification of finite-dimensional basic Hopf algebras according to their representation type 103121
- Twelve bridges from a reductive group to its Langlands dual 125143
- Some new highest weight categories 145163
- Classification of quasi-trigonometric solutions of the classical Yang–Baxter equation 155173
- The relevance and the ubiquity of Prüfer modules 163181
- Quivers and the euclidean group 177195
- eu2-Lie admissible algebras and Steinberg unitary Lie algebras 189207
- Lusztig's conjecture for finite classical groups with even characteristic 207225
- A survey on quasifinite representations of Weyl type Lie algebras 237255
- Maximal and primitive elements in baby Verma modules for type B2 257275
- Irreducible representations of the special algebras in prime characteristic 273291