For any complex number b and nonzero complex number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>, we construct a class of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$N=1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> Neveu-Schwarz algebra modules <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {L}(P,V,\lambda ,b)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">L</mi> <mo stretchy="false">(</mo> <mi>P</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> from module P over the Weyl superalgebra and restricted module V over the positive-part subalgebra of the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$N=1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> Neveu-Schwarz algebra. The necessary and sufficient conditions for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathcal {L}(P,V,\lambda ,b)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">L</mi> <mo stretchy="false">(</mo> <mi>P</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> to be irreducible are obtained. If such a module <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathcal {L}(P,V,\lambda ,b)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">L</mi> <mo stretchy="false">(</mo> <mi>P</mi> <mo>,</mo> <mi>V</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is not irreducible, we also construct its submodules concretely. Then we determine the necessary and sufficient conditions for two such Neveu-Schwarz Virasoro superalgebra modules to be isomorphic.

New Representations for the Virasoro Superalgebras

期刊论文
发表日期：

2026年2月23日

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Xiangqian Guo,
Shujuan Li,
Xuewen Liu

摘要

For any complex number b and nonzero complex number $\lambda $ $λ$ , we construct a class of $N=1$ $N = 1$ Neveu-Schwarz algebra modules $\mathcal {L}(P,V,\lambda ,b)$ $L (P, V, λ, b)$ from module P over the Weyl superalgebra and restricted module V over the positive-part subalgebra of the $N=1$ $N = 1$ Neveu-Schwarz algebra. The necessary and sufficient conditions for $\mathcal {L}(P,V,\lambda ,b)$ $L (P, V, λ, b)$ to be irreducible are obtained. If such a module $\mathcal {L}(P,V,\lambda ,b)$ $L (P, V, λ, b)$ is not irreducible, we also construct its submodules concretely. Then we determine the necessary and sufficient conditions for two such Neveu-Schwarz Virasoro superalgebra modules to be isomorphic.