Lcm of Schur indices of irreducible representations

From Groupprops
Jump to: navigation, search

Definition

For a group over a field

Suppose G is a group and K is a field whose characteristic does not divide the order of G. The lcm of Schur indices of irreducible representations of G over K is defined as the least common multiple of all the Schur index values of all the irreducible linear representations of G over K.

Typical context: finite group and splitting field

The typical context is where G is a finite group and K is a splitting field for G. In particular, the characteristic of K is either zero or is a prime not dividing the order of G, and every irreducible representation of G over any extension field of K can be realized over K.