Trace Densities and Algebraic Index Theorems for Sheaves of Formal Cherednik Algebras

Abstract We show how a novel construction of the sheaf Cherednik algebras $\mathscr {H}_{1, c, X, G}$ on quotient orbifold $Y:=X/G$ in author’s prior work leads to results for G}$, which until recently were viewed as intractable. First, every orbit type stratum $X$, we define trace density map Hochschild chain complex generalizes standard Engeli–Felder’s differential operators {D}_X$. Second, by means newly obtained maps, prove an isomorphism derived category complexes $\mathbb {C}_{Y}\llbracket \hbar \rrbracket $-modules, computes hypercohomology formal , G}$. that this is isomorphic Chen–Ruan cohomology $Y$ with values ring power series {C}\llbracket $. infer skew group 0, has well-defined Euler characteristic equal $Y$. Finally, algebraic index theorem.