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Virasoro representations with central charges $\frac{1}{2}$ and 1 on the real neutral fermion Fock space $\mathit{F^{\otimes \frac{1}{2}}}$ (1410.1186v1)

Published 5 Oct 2014 in math.RT, math-ph, math.MP, and math.QA

Abstract: We study a family of fermionic oscillator representations of the Virasoro algebra via 2-point-local Virasoro fields on the Fock space $\mathit{F{\otimes \frac{1}{2}}}$ of a neutral (real) fermion. We obtain the decomposition of $\mathit{F{\otimes \frac{1}{2}}}$ as a direct sum of irreducible highest weight Virasoro modules with central charge $c=1$. As a corollary we obtain the decomposition of the irreducible highest weight Virasoro modules with central charge $c=\frac{1}{2}$ into irreducible highest weight Virasoro modules with central charge $c=1$. As an application we show how positive sum (fermionic) character formulas for the Virasoro modules of charge $c=\frac{1}{2}$ follow from these decompositions.

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