Geodesic
Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge
Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1737-1768.

Voir la notice de l'article provenant de la source EMS Press

The vertex algebra W1+∞,c​ with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer n≥1, it was conjectured in the physics literature that W1+∞,−n​ should have a minimal strong generating set consisting of n2+2n elements. Using a free field realization of W1+∞,−n​ due to Kac-Radul, together with a deformed version of Weyl's first and second fundamental theorems of invariant theory for the standard representation of GLn​, we prove this conjecture. A consequence is that the irreducible, highest-weight representations of W1+∞,−n​ are parametrized by a closed subvariety of Cn2+2n.
DOI : 10.4171/jems/292
Classification : 17-XX, 13-XX, 00-XX
Keywords: Invariant theory, vertex algebra, W1+∞​ algebra, orbifold construction, strong finite generation 
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     title = {Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge},
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Andrew R. Linshaw. Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge. Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1737-1768. doi : 10.4171/jems/292. http://geodesic.mathdoc.fr/articles/10.4171/jems/292/

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