Minimal ring of realization of irreducible representations

From Groupprops
Revision as of 21:04, 13 July 2011 by Vipul (talk | contribs) (Created page with "==Definition== ===In characteristic zero=== Suppose <math>G</math> is a finite group and <math>R</math> is an integral domain of characteristic zero, i.e., it contains ...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Definition

In characteristic zero

Suppose G is a finite group and R is an integral domain of characteristic zero, i.e., it contains the ring of integers as a subring. We say that R is a minimal ring of realization of irreducible representations if all irreducible representations of G over some splitting field containing R can be realized with matrix entries all from R and such that no subring of R has this property.

Facts