The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 22 (Part 22)

Abstract

Let VLV_{L} be the vertex algebra associated to a non-degenerate even lattice LL, θ\theta the automorphism of VLV_{L} induced from the −1-1 symmetry of LL, and VL+V_{L}^{+} the fixed point subalgebra of VLV_{L} under the action of θ\theta. In this series of papers, we classify the irreducible weak VL+V_{L}^{+}-modules and show that any irreducible weak VL+V_{L}^{+}-module is isomorphic to a weak submodule of some irreducible weak VLV_{L}-module or to a submodule of some irreducible θ\theta-twisted VLV_{L}-module. Let M(1)+M(1)^{+} be the fixed point subalgebra of the Heisenberg vertex operator algebra M(1)M(1) under the action of θ\theta. In this paper (Part 22), we show that there exists an irreducible M(1)+M(1)^{+}-submodule in any non-zero weak VL+V_{L}^{+}-module and we compute extension groups for M(1)+M(1)^{+}.Comment: 42 pages. To appear in Journal of the Mathematical Society of Japan. We divide the article arXiv:1910.07126 into 3 parts for publication. This is the 2nd par

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