Dear Krishna, Presuming you are talking about representations over complex numbers, GAP can easily tell you with which multiplicities the irreducible representations appear in the representation P you have. For this you just need to compute its character x(P). Then computing the scalar products of x(P) with the characters of the irreducible representations (available in the character table) of your group will give you this information.
Doing the actual decomposition into the direct sum of the irreducibles is also doable by the brute-force method described e.g. in the 1st part of J.Serre's book "Linear representations of finite groups" (look for "explicit decomposition of a representation"), but there seems to be no GAP code publicly available that actually does this computation. (I wrote such code a while ago, and could e-mail it to you, although it's by no means finished or anything...) Best, Dmitrii On 19 March 2010 01:07, krishna mohan <trebauchet1...@yahoo.co.in> wrote: > Hi..... > > > Suppose I take the direct product of two two-dimensional > representations of D4...and then I want to decompose it as direct sum of > irreducible representations of D4........ > > I need to do such decompositions quite often for my current project... > > So I was wondering if GAP has anything built in to tackle the above task... > > I searched the manual but came up with nought.... > > Krishna > > > > Your Mail works best with the New Yahoo Optimized IE8. Get it NOW! > http://downloads.yahoo.com/in/internetexplorer/ > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > -- Dmitrii Pasechnik ----- DISCLAIMER: Any text following this sentence does not constitute a part of this message, and was added automatically during transmission. CONFIDENTIALITY: This email is intended solely for the person(s) named. The contents may be confidential and/or privileged. If you are not the intended recipient, please delete it, notify us, and do not copy or use it, nor disclose its contents. Thank you. Towards A Sustainable Earth: Print Only When Necessary _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
