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arXiv · 1002.4318

The invariants of the second symmetric power representation of SL_2(F_q)

Ashley Hobson·R. James Shank
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Abstract

For a prime p>2 and q=p^n, we compute a finite generating set for the SL_2(F_q)-invariants of the second symmetric power representation, showing the invariants are a hypersurface and the field of fractions is a purely transcendental extension of the coefficient field. As an intermediate result, we show the invariants of the Sylow p-subgroups are also hypersurfaces.

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Ashley Hobson, R. James Shank. 2010-02-23. The invariants of the second symmetric power representation of SL_2(F_q). https://arxiv.org/abs/1002.4318

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