> < ^ Date: Fri, 11 Feb 2000 08:36:28 -0500
> < ^ From: John Dixon <jdixon@math.carleton.ca >
< ^ Subject: Re: matrices with integer entries modulo n

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).

- John D. Dixon

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