Coinvariants and invariants of the dihedral group in characteristic

Abstract

In this paper, we completely determine the inequivalent indecomposable modular representations of the dihedral group in characteristic and also consider the structure of F[V] as the -module. As an application, we study the invariants, Hilbert ideals and coinvariants of under the low-dimensional representations. Moreover, we also describe the relations between those coinvariants and the regular representation.

Keywords:

• Dihedral group
• modular representation
• coinvariant
• Hilbert ideal

AMS SUBJECT CLASSIFICATION:

• 13A50

Acknowledgements

We would like to thank the editor and the anonymous reviewers for many helpful discussions and suggestions regarding this manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11371343], [grant number 11471090].