> ^ From:

> < ^ Subject:

rreyes wrote:

>

> I am interested in finding the irreducible representations of GL(2,n) - =

> the group of 2-by-2 invertible matrices with integer entries modulo n. =

> Here, n is not necessarily a power of a prime number. How can I use Gap =

> to find these irreducible representations?=20

>

One thing to observe is that by the Chinese Remainder Theorem GL(2,Z/nZ)

is the direct product of the groups GL(2,Z/p^eZ) where p^e is the

largest power of the prime p which divides n (taken over all primes p

dividing n). Every irreducible representation of a direct product of

groups is constructed by taken an irreducible representation of each of

the constituent groups and forming the tensor product of the

representations (see, for example, Isaacs, Character Theory of Finite

Groups, Academic Press 1976, Theorem (4.21).)

Thus the problem reduces to the case where n is a prime power. In

particular, if n is square free then we are dealing with the irreducible

representations of groups of the form GL(2,p).

> < [top]