Testing modules for irreducibility
نویسنده
چکیده
A practical method is described for deciding whether or not a nite-dimensional module for a group over a nite eld is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalisation of the Parker-Norton`Meataxe' algorithm, but it does not depend for its eeciency on the eld being small. The principal tools involved are the calculation of the nullspace and the characteristic polynomial of a matrix over a nite eld, and the factorisation of the latter. Related algorithms to determine absolute irreducibility and module isomorphism for irreducibles are also described. Details of an implementation in the GAP system, together with some performance analyses are included.
منابع مشابه
Irreducibility criterion for tensor products of Yangian evaluation modules
The evaluation homomorphisms from the Yangian Y(gln) to the universal enveloping algebra U(gln) allow one to regard the irreducible finite-dimensional representations of gln as Yangian modules. We give necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules. AMS subject classification (2000): 17B37.
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