The Bloch-Okounkov correlation functions, a classical half-integral case

TL;DR

This paper extends the calculation of Bloch-Okounkov correlation functions to the type D subalgebra at half-integral levels, linking to Gromov-Witten theory and providing new q-dimension formulas.

Contribution

It introduces the computation of correlation functions for the type D subalgebra at half-integral levels, a novel extension in the theory.

Findings

Derived correlation functions for type D at half-integral levels

Obtained q-dimension formulas for integral modules of type D

Connected correlation functions to broader mathematical theories

Abstract

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of $\hgl_\infty$-modules of level one. Recent works have calculated these character functions for higher levels for $\hgl_\infty$ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.