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Invariant theory and the 𝒲 1 + algebra with negative integral central charge

Andrew Linshaw (2011)

Journal of the European Mathematical Society

The vertex algebra 𝒲 1 + , 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 𝒲 1 + , - n should have a minimal strong generating set consisting of n 2 + 2 n elements. Using a free field realization of 𝒲 1 + , - 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 GL n ,...

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