Sylvester versus Gundelfinger
Andries E. Brouwer, Mihaela Popoviciu

TL;DR
This paper determines the exact number of generators needed for the algebra of polynomial invariants under SL_2 action on a specific module, resolving a long-standing mathematical question from 143 years ago.
Contribution
It establishes that 63 generators are necessary for the algebra of invariants of a particular SL_2-module, settling a question that has remained open for over a century.
Findings
The algebra of invariants is generated by exactly 63 elements.
The result resolves a 143-year-old open problem in invariant theory.
Provides a complete description of the minimal generating set for the algebra.
Abstract
Let be the -module of binary forms of degree and let . We show that the minimum number of generators of the algebra of polynomial functions on invariant under the action of equals 63. This settles a 143-year old question.
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