For k=0,1,2 the equivariant Chern character operators on Hilbert schemes of C^2 match vertex-operator coefficients, giving a partial verification of Okounkov's conjecture and new leading-term formulas.
On Quasimodularity of Some Equivariant Intersection Numbers on the Hilbert Schemes
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abstract
We observe that certain equivariant intersection numbers of Chern characters of tautological sheaves on Hilbert schemes for suitable circle actions can be computed using the Bloch-Okounkov formula, hence they are related to Gromov-Witten invariants of elliptic curves and its operator formalism in terms of operators on the Fock space.
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Equivariant Chern character operators and Okounkov's conjecture
For k=0,1,2 the equivariant Chern character operators on Hilbert schemes of C^2 match vertex-operator coefficients, giving a partial verification of Okounkov's conjecture and new leading-term formulas.