Irreducible Virasoro modules from tensor products

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Here we consider the particular case of affine surfaces V admitting smooth completions (S,B S ). Indeed, by the Danilov-Gizatullin Isomorphy Theorem [14], the isomorphy type as

All unitary irreducible representations (u. r.’s) of groups which are semidirect products with abelian normal subgroup, are known to be.. induced representations,

Fix T e P^ and let V\ denote the associated variety of the unitary module L(T+^O)). We are now almost ready to do this but there is one more catch. Assuming this holds we can

Verdier, Reflexive modules over rational double points, Math.. Auslander, Functors and morphisms determined by objects,

It is already shown that each semi-simple coherent family contains an infinite dimensional simple highest weight module relative to some basis (Proposition 5.8).. In this section,

We may assume (by hypothesis on X) that X is irreducible, and even connected and normal (so it is normal after any extension ofscalars on fc, by Theorem 3.3.6). By Corollary 3.2.3,

D Even though in general the topology on the spaces of analytic and hyperfunction vectors is hard to get a hand on, one has a quite good picture for unitary highest