We establish an isomorphism between the center of the twisted Heisenberg category and the subalgebra \(\Gamma \) of the symmetric functions generated by odd power sums. We give a graphical description of the factorial Schur Q-functions and inhomogeneous power sums as closed diagrams in the twisted Heisenberg category and show that the bubble generators of the center correspond to two sets of generators of \(\Gamma \) which encode data related to up/down transition functions on the Schur graph. Finally, we describe an action of the trace of the twisted Heisenberg category, the W-algebra \(W^-\subset W_{1+\infty }\), on \(\Gamma \).

我们在扭曲的海森堡类别的中心与由奇次幂和生成的对称函数的子代数\（\ Gamma \）之间建立同构。我们以扭曲的Heisenberg类别的闭合图的形式，对阶乘Schur Q函数和不均匀功率和进行图形化描述，并显示出中心的气泡生成器对应于\（\ Gamma \）的两组生成器，它们对与数据相关的数据进行编码到Schur图上的上/下过渡功能。最后，我们描述了扭曲的Heisenberg类（W-代数\（W ^-\子集W_ {1+ \ infty} \））对\（\ Gamma \）的迹的作用。