Algebraic analysis demonstrates an isomorphism between D4 triality invariants and joint covariants of binary cubic and quadratic forms, highlighting connections in invariant theory.
D₄ triality invariants are modular forms as well as invariant polynomials for a fiber product of the modular group and the Weyl group of type F₄ . We show that the ring of D₄ triality invariants satisfying a certain cusp condition is isomorphic to the ring of joint covariants of a binary cubic and a binary quadratic form.
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Kazuhiro Sakai (2026) studied this question.
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