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E. B. Feigin Lebedev Physics Institute Moscow, Russia evgfeig@gmail.com

The PBW filtration
We study the PBW filtration on irreducible integrable highest weight representations of an affine Kac-Moody algebra g . The n-th space of this filtration is spanned with the vectors x1 . . . xs v , where xi g , s n and v is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations. For g of the type A1 we prove our conjecture and derive the fermionic formula for the graded character.

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