The invariants of the third symmetric power representation of SL_2(F_p)
Ashley Hobson, R. James Shank
TL;DR
This paper computes the invariants of the third symmetric power representation of SL_2(F_p) for primes p>3, using SAGBI bases and Hilbert series calculations to identify a finite generating set.
Contribution
It introduces a method to explicitly determine the invariants of the third symmetric power representation of SL_2(F_p) for primes greater than 3, employing SAGBI bases and Hilbert series.
Findings
Finite generating set for SL_2(F_p)-invariants identified
Construction of an infinite SAGBI basis demonstrated
Hilbert series used to facilitate invariant computation
Abstract
For a prime p>3, we compute a finite generating set for the SL_2(F_p)-invariants of the third symmetric power representation. The proof relies on the construction of an infinite SAGBI basis and uses the Hilbert series calculation of Hughes and Kemper.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Coding theory and cryptography · Finite Group Theory Research