On some integral representations of groups and global irreducibility

Document Type : Ischia Group Theory 2016

Author

UWI, Mona, Kingston

Abstract

Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to arithmetic rings. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed. Let $K$ be a finite extension of the rational number field and $O_K$ the ring of integers of $K$. Let $G$ be a finite subgroup of $GL(2,K)$, the group of $(2 \times 2)$-matrices over $K$. We obtain some conditions on $K$ for $G$ to be conjugate to a subgroup of $GL(2,O_K)$.

Keywords

Main Subjects


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Volume 7, Issue 3 - Serial Number 3
Proceedings of the Ischia Group Theory 2016-Part III
September 2018
Pages 81-94
  • Receive Date: 30 November 2016
  • Revise Date: 21 November 2017
  • Accept Date: 23 November 2017
  • Published Online: 01 September 2018