Related papers: Construction of Vector Valued Modular Forms from J…

We introduce a new multivariate orthogonal polynomial which is a 2-parameter deformation of the spherical polynomial by harmonic analysis on symmetric cone. This is also regarded as a multivariate analogue of the circular Jacobi polynomial.…

We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. The key ingredient is a characterization of the Demazure…

We show that Hida's families of $p$-adic elliptic modular forms generalize to $p$-adic families of Jacobi forms. We also construct $p$-adic versions of theta lifts from elliptic modular forms to Jacobi forms. Our results extend to Jacobi…

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical…

We focus on the problem of producing new modular tensor categories from Hopf algebras. To do this, we first give a general method to construct factorizable Hopf algebras. Then we apply the method to construct two families of ribbon…

We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\G$ of $SL(2, \bR)$…

We give a characterisation of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a…

In the paper we study two types of relations: a one is between the elliptic genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac-Moody…

The problem on the construction of antisymmetric paramodular forms of canonical weight 3 was open since 1998. Any cusp form of this type determines a canonical differential form on any smooth compactification of the moduli space of Kummer…

Let $D$ be an odd square-free positive integer and $C$ a divisor of $D$. For any quadratic character $\chi$ modulo $C$, we prove that the $\chi$-part of the group $J_0(DC)_\text{tor}$ of torsion points of $J_0(DC)$ coincides with the…

We compare modular forms of characteristic $p>0$ (i.e. Drinfeld's modular forms) and automorphic forms. We prove that spaces of these modular forms (which are of characteristic $p$) can be described by function spaces of characteristic…

In this paper, we compute basis elements of certain spaces of weight 0 weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the…

We present a formula for vector-valued modular forms, expressing the value of the Hilbert-polynomial of the module of holomorphic forms evaluated at specific arguments in terms of traces of representation matrices, restricting the weight…

For any discrete group $\Gamma$ and any 2-dimensional complex representation $\rho$ of $\Gamma$, we introduce the notion of $\rho-$equivariant functions, and we show that they are parameterized by vector-valued modular forms. We also…

Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a…

We show that some $q$-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion…

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces…

Let $V$ be a strongly regular vertex operator algebra. For a state $h \in V_1$ satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions Tr$_Mq^{L(0)-c/24}\zeta^{h(0)} ($M$ a $V$-module) is a…

We construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional N=(2,2) supersymmetric theories. They arise in a family labeled by two integers N and k which…

We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence…