nLab transvectant

Certain invariant bilinear differential operators used to obtain new invariants of bilinear forms from old, discovered by Gordan,

• P. Gordan, Das Zerfallen der Curven in gerade Linien, Math. Ann., 45 (1894) 411-427

Appearance of transvectants is related to certain transformations on symmetric spaces, transvections.

Transvectants in the context of modular forms are Rankin-Cohen brackets.

• P.J. Olver, J.A. Sanders, Transvectants, modular forms and the Heisenberg algebra, Adv. Appl. Math., 25 (2000) 252-283 doi
• V. Ovsienko, P. Redou, Generalized transvectants-Rankin–Cohen brackets Lett. Math. Phys. 63, 19–28 (2003). https://doi.org/10.1023/A:1022956710255
• P.J. Olver, M. Petitot, P. Solé, Generalized transvectants and Siegel modular forms, Advances in Applied Mathematics 38:3 (2007) 404-418 doi (preprint pdf)
• Sofiane Bouarroudj, Dimitry A. Leites, Invariant differential operators in positive characteristic, J. Algebra 499 (2018) 281-297 doi
• G. Mari Beffa, Jan A. Sanders, Transvection and differential invariants of parametrized curves, J. Lie Theory 18 (2008) 93–123