Mirko Primc
Combinatorial Bases of Modules for Affine Lie Algebra $B_2\sp{(1)}$
Preprint series: ESI preprints

MSC:

17B67 Kac-Moody algebras (structure and representation theory)

17B99 None of the above but in this section

05A19 Combinatorial identities

Abstract: In this paper we construct bases of standard modules $L(\Lambda)$
for affine Lie algebra of type $B_2\sp{(1)}$ consisting of
semi-infinite monomials. The main technical ingredient is a
construction of monomial bases for Feigin-Stoyanovsky's subspaces
$W(\Lambda)$ of $L(\Lambda)$ by using simple currents and
intertwining operators in vertex operator algebra theory. By
coincidence $W(k\Lambda_0)$ for $B_2\sp{(1)}$ and the standard
module $L(k\Lambda_0)$ for $A_1\sp{(1)}$ have the same presentation
$\mathcal P/\mathcal I$\,, so our main theorem provides a new proof
of linear independence of monomial bases of $A_1\sp{(1)}$-modules
$L(k\Lambda_0)$.