The PBW filtration

2007/02/26 by E. Feigin, Feigin, E.
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0702797

18 pages

arxiv created 2007/02/26 · arxiv updated 2009/12/01

Abstract

In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebra \gh. The n-th space of this filtration is spanned with the vectors x₁... x_s v, where x_i∈\gh, 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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