Lcm of Schur indices of irreducible representations
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 .