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arxiv: 0910.1991 · v1 · submitted 2009-10-11 · 🧮 math.RT · math.GR

On the Decomposition Numbers of the Ree Groups 2F4(q²) in Non-Defining Characteristic

classification 🧮 math.RT math.GR
keywords decompositionmatricesgroupsl-modularprimescharacteristiccharacterscompute
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We compute the l-modular decomposition matrices of the simple Ree groups 2F4(q^2), where q^2=2^{2n+1} and n is a positive integer, for all primes l > 3 up to some entries in the unipotent characters. Using these matrices we determine the smallest degree of a non-trivial irreducible l-modular representation of 2F4(q^2) for all primes l > 3. We also obtain results on the 3-modular decomposition matrices of 2F4(q^2).

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