Geodesic
Explicit equations for exterior square of the general linear group
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 33, Tome 470 (2018), pp. 120-137

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We present several explicit systems of equations defining exterior square of the general linear group $\wedge^2\mathrm{GL}_n$ as an affine group scheme. Algebraic ingredients of the equations, exterior numbers, are translated into the language of weight diagrams corresponding to Lie groups of type $A_{n-1}$ in representation with the highest weight $\varpi_2$. 
@article{ZNSL_2018_470_a7,
     author = {R. A. Lubkov and I. I. Nekrasov},
     title = {Explicit equations for exterior square of the general linear group},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {120--137},
     publisher = {mathdoc},
     volume = {470},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_470_a7/}
}
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R. A. Lubkov; I. I. Nekrasov. Explicit equations for exterior square of the general linear group. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 33, Tome 470 (2018), pp. 120-137. http://geodesic.mathdoc.fr/item/ZNSL_2018_470_a7/