3 years ago

Koszul properties of the moment map of some classical representations

Aldo Conca, Hans-Christian Herbig, Srikanth B. Iyengar


This work concerns the moment map \(\mu \) associated with the standard representation of a classical Lie algebra. For applications to deformation quantization it is desirable that \(S/(\mu )\) , the coordinate algebra of the zero fibre of \(\mu \) , be Koszul. The main result is that this algebra is not Koszul for the standard representation of \(\mathfrak {sl}_{n}\) , and of \(\mathfrak {sp}_{n}\) . This is deduced from a computation of the Betti numbers of \(S/(\mu )\) as an S-module, which are of interest also from the point of view of commutative algebra.

Open access
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