Hilbert Series and Degree Bounds in Invariant Theory
نویسنده
چکیده
The Hilbert series and degree bounds play signiicant roles in computational invariant theory. In the modular case, neither of these tools is available in general. In this article three results are obtained, which provide partial remedies for these shortcomings. First, it is shown that the so-called extended Hilbert series, which can always be calculated by a Molien type formula, yields strong constraints on the degrees of primary invariants. Then it is shown that for a trivial source module the (ordinary) Hilbert series coincides with that of a lift to characteristic 0 and can hence be calculated by Molien's formula. The last result is a generalization of GG obel's degree bound to the case of monomial representations.
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