Vertices for Iwahori-Hecke algebras and the Dipper-Du conjecture. (English) Zbl 1468.20026
Summary: Let \(\mathcal{H}_n\) denote the Iwahori-Hecke algebra corresponding to the symmetric group \(\mathfrak{S}_n\). We set up a Green correspondence for bimodules of these Hecke algebras, and a Brauer correspondence between their blocks. We examine Specht modules for\(\mathcal{H}_n\) and compute the vertex of certain Specht modules, before using this to give a complete classification of the vertices of blocks of \(\mathcal{H}_n\) in any characteristic. Finally, we apply this classification to resolve the Dipper-Du conjecture about the structure of vertices of indecomposable \(\mathcal{H}_n\)-modules.
MSC:
| 20C30 | Representations of finite symmetric groups |
| 16G99 | Representation theory of associative rings and algebras |
| 20C08 | Hecke algebras and their representations |
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