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

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

2010-02-23

arxiv.org/abs/1002.4318v1

Mathematics

Commutative Algebra

Scientific paper

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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