Simple weak modules for some subalgebras of the Heisenberg vertex algebra and Whittaker vectors

Abstract

Let $\mathcal{M}(p)$ $(p=2,3,\dots )$ be the singlet vertex operator algebra and $\omega$ its conformal vector. We classify the simple weak $\mathcal{M}(p)$-modules with a non-zero element $u$ such that for some integer $s\ge 2$, ${\omega }_{i}u\in \mathbb{C}u$ ($i=\lfloor s/2\rfloor +1,\lfloor s/2\rfloor +2,\dots ,s-1$), ${\omega }_{s}u\in {\mathbb{C}}^{\times }u$, and ${\omega }_{i}u=0$ for all $i>s$.

21 pages. arXiv admin note: text overlap with arXiv:1608.07890

References in corpus (3)

• Whittaker modules for the affine Lie algebra $A_1^{(1)}$
• Logarithmic intertwining operators and W(2,2p-1)-algebras
• Simple weak modules for the fixed point subalgebra of the Heisenberg vertex operator algebra of rank $1$ by an automorphism of order $2$ and Whittaker vectors