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.
A short note on a conjecture of Okounkov about a q-analogue of multiple zeta values
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abstract
In [Ok] Okounkov studies a specific $q$-analogue of multiple zeta values and makes some conjectures on their algebraic structure. In this note we compare Okounkovs $q$-analogues to the generating function for multiple divisor sums defined in [BK1]. We also state a conjecture on their dimensions that complements Okounkovs conjectural formula and present some numerical evidences for it.
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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.