标题： N=1 Bondi-Metzner-Sachs 超代数上的光滑模 显示英文标题

标题： Smooth modules over the N=1 Bondi-Metzner-Sachs superalgebra

摘要： 在本文中，我们提出了N=1 Bondi-Metzner-Sachs (BMS) 超代数上对变形式的行列式公式。该公式建立了Verma模不可约性的必要且充分条件。然后，我们引入并表征了一类推广了N=1 BMS超代数上Verma模和Whittaker模的简单光滑模。我们还利用Heisenberg-Clifford顶点超代数构造了N=1 BMS超代数的自由场实现。这种自由场实现使我们能够得到N=1 BMS超代数的一族自然光滑模，其中包括Fock模和某些Whittaker模。 显示英文摘要

摘要： In this paper, we present a determinant formula for the 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.