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

The Bloch-Okounkov correlation functions of negative levels

Bloch and Okounkov introduced an $n$-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible $\hat{gl}_\infty$-modules of level one. These correlation functions have been generalized for irreducible integrable modules of $\hat{gl}_\infty$ and its classical Lie subalgebras of positive levels by the authors. In this paper we extend further these results and compute the correlation functions as well as the $q…

The Bloch-Okounkov correlation functions at higher levels

We establish an explicit formula for the n-point correlation functions in the sense of Bloch-Okounkov for the irreducible representations of $\hat{gl}_\infty$ and $W_{1+\infty}$ of arbitrary positive integral levels.

The Bloch-Okounkov correlation functions of classical type

Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc, and it can also be interpreted as correlation functions on integrable gl_\infty-modules of level one. Such gl_\infty-correlation functions at higher levels were then calculated by Cheng and Wang. In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable …

量子差分方程与仿射型 $A$ 的 Maulik-Okounkov 量子仿射代数

Quantum difference equations and Maulik-Okounkov quantum affine algebras of affine type $A$

本文通过 Dubrovin 联络的单值表示，证明了量子环面代数与仿射型 $A$ 的 Maulik-Okounkov 量子仿射代数正半部分同构，其核心在于证明代数与几何量子差分方程具有相同的退化极限。

多重q-zeta值与迹

Multiple q-zeta values and traces

本文推广Bloch与Okounkov关于迹与拟模形式关系的结果，证明多类迹对应多重q-zeta值，其简单情形验证了形变Bloch-Okounkov 1点函数的系数性质。

Formal differential operators, vertex operator algebras and zeta--values , II

We introduce certain correlation functions (graded $q$--traces) associated to vertex operator algebras and superalgebras which we refer to as $n$--point functions. These naturally arise in the studies of representations of Lie algebras of differential operators on the circle \cite{Le1}--\cite{Le2}, \cite{M}. We investigate their properties and consider the corresponding graded $q$--traces in parallel with the passage from genus 0 to genus 1 conformal field theory. By using the vertex operator algebra theory we analyze in detail correlation functions in some particular cases. We obtain elliptic…