Lcm of Schur indices of irreducible representations
From Groupprops
Definition
For a group over a field
Suppose is a group and
is a field whose characteristic does not divide the order of
. The lcm of Schur indices of irreducible representations of
over
is defined as the least common multiple of all the Schur index values of all the irreducible linear representations of
over
.
Typical context: finite group and splitting field
The typical context is where is a finite group and
is a splitting field for
. In particular, the characteristic of
is either zero or is a prime not dividing the order of
, and every irreducible representation of
over any extension field of
can be realized over
.