Combinatorial bases of modules for affine Lie algebra B_2^(1)

Abstract

In this paper we construct bases of standard (i.e. integrable highest weight) 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 type 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 integrable highest weight module $L(k{\Lambda }_0)$ for $A_1\sp{(1)}$ have the same parametrization of combinatorial bases and the same presentation $\mathcal{P}/\mathcal{I}$\,.

AMS-LaTeX, 29 pages, to appear in Central European Journal of Mathematics. v2: The claim that presentation for B_2^(1) implies linear independence for A_1^(1) is incorrect and omitted; other minor changes; a new section on vertex operator formula is added

References in corpus (1)

• Simple currents and extensions of vertex operator algebras