3 problems

Let $A=k_{-1}[x_1,\dots,x_n]$, and let $G$ act by permutations of the generators. A bireflection is an automorphism whose trace function has a pole of order $n-2$ at $t=1$; equival…

Let $B$ be a quantum polynomial ring and let $G$ be a finite subgroup of $\operatorname{Aut_{gr}}(B)$ such that the fixed subring $B^G$ has finite global dimension. For a positive…

Let $B$ be a quantum polynomial ring and let $G$ be a finite subgroup of $\operatorname{Aut_{gr}}(B)$. Noncommutative Shephard–Todd–Chevalley conjecture. The fixed subring $B^G$ ha…