The PBW filtration

DOI10.1090/S1088-4165-09-00349-5arXivmath/0702797MaRDI QIDQ6478870

Publication date: 26 February 2007

Abstract: In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebra

g h

. The

n

-th space of this filtration is spanned with the vectors

x_{1} . . . x_{s} v

, where

x_{i} i n g h

,

s l e 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.

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

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