The invariants of the second symmetric power representation of SL₂(F_q)
classification
🧮 math.AC
math.RT
keywords
invariantsfieldpowerrepresentationsecondsymmetriccoefficientcompute
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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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