Tensor products of irreducible representations of the group G = GL(3,q)

Details Tensor products of irreducible representations of the group G = GL(3,q) Tensor products of irreducible representations of the group G = GL(3,q)

2009-01-02

arxiv.org/abs/0901.0292v1

Mathematics

Representation Theory

amsart, 10 pages, no figures, submitted to manuscripta mathematica

Scientific paper

We describe the tensor products of two irreducible linear complex representations of the finite general linear group G = GL(3,q) in terms of induced representations by linear characters of maximal torii and also in terms of Gelfand-Graev representations. Our results include MacDonald's conjectures for G and at the same time they are extensions to G of finite counterparts to classical results on tensor products of holomorphic and anti-holomorphic representations of the group SL(2, R). Moreover they provide an easy way to decompose these tensor products, with the help of Frobenius reciprocity. We also state some conjectures for the general case of GL(n,q).

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