We define a notion of formal quantum field theory and associate a formal quantum field theory
to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces.
This enables us to find an effective way to compute K-theoretical intersection theories on Hilbert schemes
via a connection to Macdonald polynomials and vertex operators.
We propose some conjectures on the generating
series of (equivariant) Euler characteristics of some vector bundles constructed from the tautological
bundles on Hilbert schemes of points on affine $k$-spaces.
We establish the surface case of these conjectures
and present some verifications of the higher dimensional cases.
Qi'an GuanBeijing International Center for Mathematical Research, and School of Mathematical Sciences, Peking UniversityXiangyu ZhouInstitute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences
Algebraic GeometryComplex Variables and Complex Analysismathscidoc:1806.01001