arXiv math/07027972007-02-26math.QAmath.RT

The PBW filtration

E. Feigin

备注：: 18 pages

英文摘要：

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 $x_1... x_s v$, where $x_i\in\gh$, $s\le n$ 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 $A_1$ we prove our conjecture and derive the fermionic formula for the graded character.

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