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This question is follow up of this MO-post. First let us recall the necessary definitions. A function $f:X\to X$ on a group $X$ is called a polynomial if there exists $n\in\mathbb N$ and elements $a_0,...

(This is an old MSE question from me, which did not get any answer, and when looking back seems interesting to post it here:) Let $G$ be a finite group. Consider the set $X_G:=\cup_{H\le G} G/H$, ...

The functions $p^*_k(x)=\sum_{i=1}^N ((x_i-i)^k-(-i)^k)$ are analogues of power sum symmetric functions, called shifted symmetric by Okounkov and Olshanski. Define $p^*_{(k_1,k_2,...)}=p^*_{k_1}p^*_{...