Related papers: From Vertex Operators to Calogero-Sutherland Model…
We prove index formulas for elliptic operators acting between sections of C*-vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from K-theory of a C*-algebra to de Rham homology of smooth subalgebras. We…
Associated to a presentable $\infty$-category $\mathcal{C}$ and an object $X \in \mathcal{C}$ is the tangent $\infty$-category $\mathcal{T}_X\mathcal{C}$, consisting of parameterized spectrum objects over $X$. This gives rise to a…
Some integration formulas which either occur or are implicit in Ha's recent exact calculation of some correlations in the Calogero-Sutherland model are discussed. These integration formulas include the calculation of the inner product…
If a vertex operator algebra $V=\oplus_{n=0}^{\infty}V_n$ satisfies $\dim V_0=1, V_1=0$, then $V_2$ has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative)…
In this note we show that the irreducible twisted modules of a holomorphic, $C_2$-cofinite vertex operator algebra $V$ have $L_0$-weights at least as large as the smallest $L_0$-weight of $V$. Hence, if $V$ is of CFT-type, then the twisted…
From the defining exchange relations of the A_{q,p}(gl_{N}) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions relating the parameters p,q,N and the central…
We describe Zhu recursion for a vertex operator algebra (VOA) and its modules on a genus $g$ Riemann surface in the Schottky uniformisation. We show that $n$-point (intertwiner) correlation functions are written as linear combinations of…
In this work we introduce a new combinatorial notion of boundary $\Re C$ of an $\omega$-dimensional cubing $C$. $\Re C$ is defined to be the set of almost-equality classes of ultrafilters on the standard system of halfspaces of $C$, endowed…
A closure operator on a set $X$ is a function $\operatorname{cl}: \wp(X) \to \wp(X)$ satisfying, for all $A, B \subseteq X$, the following properties: extensivity, $A \subseteq \operatorname{cl}(A)$; monotonicity, which states that if $A…
Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized…
We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…
This paper is about the orbifold theory for vertex operator superalgebras. Given a vertex operator superalgebra V and a finite automorphism group G of V, we show that the trace functions associated to the twisted sectors are holomorphic in…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…
We show that the $C^*$-algebra generated by the field operators associated to a symplectic space $\Xi$ is graded by the semilattice of all finite dimensional subspaces of $\Xi$. If $\Xi$ is finite dimensional we give a simple intrinsic…
We compute the partition and correlation generating functions for the Heisenberg intertwiner generalized vertex operator algebra on a genus $g$ Riemann surface in the Schottky uniformization. These are expressed in terms of differential…
In this article which is the first of a series of three, we consider $\mathcal W({\mathfrak{sl}_d})$-symmetric conformal field theory in topological regimes for a generic value of the background charge, where $\mathcal W({\mathfrak{sl}_d})$…
For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form $A=\left(\begin{array}{cc} 0 & -C^{*}\\ C & 0 \end{array}\right)$, where $C:D\left(C\right)\subseteq H_{0}\to…
In our paper~\cite{KR} we began a systematic study of representations of the universal central extension $\widehat{\Cal D}\/$ of the Lie algebra of differential operators on the circle. This study was continued in the paper~\cite{FKRW} in…
Let $X$ be a finite connected graph, each of whose vertices has degree at least three. The fundamental group $\Gamma$ of $X$ is a free group and acts on the universal covering tree $\Delta$ and on its boundary $\partial \Delta$, endowed…
Suppose a Lie group $G$ acts on a vertex algebra $V$. In this article we construct a vertex algebra $\tilde{V}$, which is an extension of $V$ by a big central vertex subalgebra identified with the algebra of functionals on the space of…