Smooth modules over the N = 1 Bondi–Metzner–Sachs superalgebra

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2024-05-10 DOI:10.1142/s0219199724500214

Dong Liu, Yufeng Pei, Limeng Xia, Kaiming Zhao

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引用次数: 0

Abstract

In this paper, we present a determinant formula for a contravariant form on Verma modules over the $N = 1$ Bondi–Metzner–Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the $N = 1$ BMS superalgebra. We also utilize the Heisenberg–Clifford vertex superalgebra to construct a free field realization for the $N = 1$ BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the $N = 1$ BMS superalgebra, which includes Fock modules and certain Whittaker modules.

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N = 1 邦迪-梅兹纳-萨克斯超代数上的光滑模块

在本文中，我们提出了关于 N=1 邦迪-梅兹纳-萨克斯（BMS）超代数上的维尔马模块的协变形式的行列式。该公式为 Verma 模块的不可还原性建立了必要条件和充分条件。然后，我们引入并描述了一类简单光滑模块，它们概括了 N=1 BMS 上代数的 Verma 模块和 Whittaker 模块。我们还利用海森堡-克利福德顶点超代数构建了 N=1 BMS 超代数的自由场实现。通过这个自由场实现，我们可以得到 N=1 BMS 上代数的自然光滑模块族，其中包括福克模块和某些惠特克模块。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.