Related papers: The Fine Structure of Translation Functors

We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) the weight of any nonzero…

We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness…

The non-trivial zeros of the Riemann zeta function and the prime numbers can be plotted by a modified von Mangoldt function. The series of non-trivial zeta zeros and prime numbers can be given explicitly by superposition of harmonic waves.…

We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…

We show that C_2-cofiniteness is enough to prove a modular invariance property of vertex operator algebras without assuming the semisimplicity of Zhu algebra. For example, if a VOA V=\oplus_{m=0}^{\infty}V_m is C_2-cofinite, then the space…

In this paper we obtain explicit formulas for mock theta functions $\Phi^{[m,s]}(\tau, z_1, z_2,t)$ $(m \in \frac12 \mathbf{N}, s \in \frac12 \mathbf{Z})$ by using the coroot lattice of the Lie superalgebra $D(2,1,a)$ and the Kac-Peterson's…

The conformal transformations with respect to the metric defining the orthogonal Lie algebra o(n) give rise to a one-parameter (c) family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra…

Suppose that $\ell \geq 5$ is prime. For a positive integer $N$ with $4 \mid N$, previous works studied properties of half-integral weight modular forms on $\Gamma_0(N)$ which are supported on finitely many square classes modulo $\ell$, in…

We construct a Fourier--Mukai transform for smooth complex vector bundles $E$ over a torus bundle $\pi:M \to B,$ the vector bundles being endowed with various structures of increasing complexity. At a minimum, we consider vector bundles $E$…

We show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight…

Let g_A (respectively, g_A(\mu)) be the graded multi-loop Lie algebra (respectively graded twisted multi-loop Lie algebra)" associated with the simple finite dimensional Lie algebra g over the complex field C. In this paper, we prove that…

This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…

We use a q-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan's tau function which involves t-cores and a new class of partitions which we call (m,k)-capsids. The same method can be applied in conjunction with…

We use the formalism of the Bergman tau functions to study the geometry of moduli spaces of holomorphic quadratic differentials on complex algebraic curves. We introduce two natural tau functions and interpret them as holomorphic sections…

Recent Quality Estimation (QE) models based on multilingual pre-trained representations have achieved very competitive results when predicting the overall quality of translated sentences. Predicting translation errors, i.e. detecting…

Let g be a finite dimensional complex semisimple Lie algebra, and let V be a finite dimensional represenation of g. We give a closed formula for the mth Frobenius-Schur indicator, m>1, of V in representation-theoretic terms. We deduce that…

Let $N_{k} (\g)$ be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type $A_{\ell -1} ^{(1)}$ or $C_{\ell} ^{(1)}$. We construct a family of ideals $J_{m,n} (\g)$ in $N_{k} (\g)$, and a…

In this article, we focus on the left (translation) actions on noncommutative compact connected Lie groups ${\rm SU}(2) \times T^n$. We define the rotation vectors of the left actions induced by the elements in the maximal tori of ${\rm…

We study the category $\mathcal{O}$ for a general Coxeter system using a formulation of Fiebig. The translation functors, the Zuckerman functors and the twisting functors are defined. We prove the fundamental properties of these functors,…

This is a review of the authors' recent results on an integrable structure of the melting crystal model with external potentials. The partition function of this model is a sum over all plane partitions (3D Young diagrams). By the method of…