Related papers: The Fine Structure of Translation Functors

If $\fg$ is a semisimple Lie algebra, we describe the prime factors of $\mcU(\fg)$ that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also…

Let $\mathcal{M}$ be a semifinite von Neumann algebra and let $E$ be a symmetric function space on $(0,\infty)$. Denote by $E(\mathcal{M})$ the non-commutative symmetric space of measurable operators affiliated with $\mathcal{M}$ and…

Toroidal Lie algebras are universal central extentions of the finite dimensional simple Lie algbera tensored with Laurent Polynomials in several commuteing variables. In this paper we classify irreducible integrable modules for Toroidal Lie…

We demonstrate a new, hybrid symbolic-numerical method for the automatic synthesis of all families of translation operators required for the execution of the Fast Multipole Method (FMM). Our method is applicable in any dimensionality and to…

Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category $\mathcal{C}$ and a central charge $c$. A long-term goal is to classify unitary rational conformal field theories…

This paper develops the homological backbone of the theory of non-commutative $n$-ary $\Gamma$-semirings. Starting from an $n$-ary $\Gamma$-semiring $(T,+,\tilde{\mu})$ and its $\Gamma$-ideals, we work in the slot-sensitive categories of…

Given a Lie superalgebra $\frak g$ with a subalgebra $\frak g_{\geq 0}$, and a finite-dimensional irreducible $\frak g_{\geq 0}$-module $F$, the induced $\frak g$-module $M(F)=U({\frak g}) \otimes_{U(\frak g_{\geq 0})} F $ is called a…

We introduce a novel approach for computing the twist operator correlators (TOC) in two-dimensional conformal field theories (2d CFT) and the closely related isomonodromic tau functions. The method stems from the formal path integral…

Write $\Theta^E$ for the stable character associated to a finite dimensional representation $E$ of a connected real reductive group $G$. Let $M$ be the centralizer of a maximal torus $T$, and denote by $\Phi_M(\gm,\Theta^E)$ Arthur's…

We generalize the notion of an intertwining operator to N-graded weak modules over a vertex operator algebra and study their properties. We show a formula for the dimensions of these intertwining operators in terms of modules over the Zhu…

We study rather general multiple zeta-functions whose denominators are given by polynomials. The main aim is to prove explicit formulas for the values of those multiple zeta-functions at non-positive integer points. We first treat the case…

We explore two solutions to the problem of mistranslating rare words in neural machine translation. First, we argue that the standard output layer, which computes the inner product of a vector representing the context with all possible…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

The experimental sensitivity to $\mu \to e$ conversion on nuclei is set to improve by four orders of magnitude in coming years. However, various operator coefficients add coherently in the amplitude for $\mu \to e$ conversion, weighted by…

We construct vertex operator representations for the full (N+1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl(N)…

In this paper, we determine the complex-valued solutions of the functional equation $$ f(x\sigma(y))+f(\tau(y)x)=2f(x)f(y)$$ for all $x,y \in M$, where $M$ is a monoid, $\sigma$: $M\longrightarrow M$ is an involutive automorphism and…

We calculate the prediction for the anomalous weak-magnetic form factor of the tau lepton at $q^2=M_Z^2$ within the Standard Model. With all particles on-shell, this is a electroweak gauge invariant quantity. Its value is $a_\tau^w (M_Z^2)=…

We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras $\hgltwo$, $\hC$ and $\hD$, and determine the necessary and sufficient conditions for quasi-finite irreducible highest weight modules…

Magnetic translation groups are considered as central extensions of the translation group T=Z^n by the group of factors (a~gauge group) U(1). The obtained general formulae allow to consider a magnetic field as an~antisymmetric tensor (of…

Let V^L and V^R be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let F be a conformal full field algebra over the tensor product of V^L and V^R. We…