Hidden $SL_2(\mathbb{Z})$-symmetry in $BC_l^{(2)}$

Abstract

A well-known \(\Gamma_\theta\)-action on the characters of integrable highest weight modules over the affine Lie algebra of type \(BC_l^{(2)}\) at a positive level is extended to an \(\mathrm{SL}_2(\mathbb{Z})\)-action at a positive even level by supplementing their twisted characters.