Abstract:
I give a general formula for the Hilbert series of a polarised $n$-dimensional orbifold (for example, with isolated orbifold points). The result comes from orbifold RR, and so ultimately from equivariant RR (the Atiyah--Singer Lefschetz trace formula); however, the formula is organised so that no Chern or Todd classes appear explicitly, and no Dedekind sums. The formula reduces much of my work over 20 years to a few lines of computer algebra.
If time and the state of current work permits, I hope to add some observations about orbifold RR as a polynomial function (with integral
coefficients) on orbifold K theory.
