  The direct sum of irreducible level one integrable representations of affine
Kac-Moody Lie algebra of (affine) type $ADE$ carries a structure of
$P/Q$-graded vertex operator algebra. There exists a filtration on this direct
sum studied by Kato and Loktev such that the corresponding graded vector space
is a direct sum of global Weyl modules. The associated graded space with
respect to the dual filtration is isomorphic to the homogenous coordinate ring
of semi-infinite flag variety. We describe the ring structure in terms of
vertex operators and endow the homogenous coordinate ring with a structure of
$P/Q$-graded vertex operator algebra. We use the vertex algebra approach to
derive semi-infinite Pl\"ucker-type relations in the homogeneous coordinate
ring.
