Related papers: Pullback formula for vector-valued Hermitian modul…

Given an n x n matrix over the ring of differential polynomials F(t)[\D;\delta], we show how to compute the Hermite form H of A, and a unimodular matrix U such that UA=H. The algorithm requires a polynomial number of operations in terms of…

We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued Jacobi forms (both in the orthogonal and Hermitian…

We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…

While vector-valued automorphic forms can be defined for an arbitrary Fuchsian group $\Gamma$ and an arbitrary representation $R$ of $\Gamma$ in GL$(n,{\mathbb C})$, their existence has been established in the literature only when…

In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…

We study a class of meromorphic modular forms characterised by Fourier coefficients that satisfy certain divisibility properties. We present new candidates for these so-called magnetic modular forms, and we conjecture properties that these…

We study the pullback maps on cohomology groups for equivariant rational maps (i.e., monomial maps) on toric varieties. Our method is based on the intersection theory on toric varieties. We use the method to determine the dynamical degrees…

We construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2,1) over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.

We show that the category of categories with pullbacks and pullback preserving functors is cartesian closed.

We introduce a very simple, exactly solvable PT-symmetric non-Hermitian model with real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is…

In this note, we consider discriminant forms that are given by the norm form of real quadratic fields and their induced Weil representations. We prove that there exists an isomorphism between the space of vector-valued modular forms for the…

In this paper we follow the constructions of Turaev's book [Tu] closely, but with small modifications, to construct of a modular functor, in the sense of Kevin Walker, from any modular tensor category. We further show that this modular…

We prove an extension of the Quillen Theorem Bn for homotopy fibres to a similar result for homotopy pullbacks and use this to obtain sufficient conditions on a pullback diagram of categories to guarantee that it be a homotopy pullback.

We investigate hermitian Yang-Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions with connected fibres. Under some technical assumptions on the graded object of a…

We consider the genus of $20$ classes of unimodular Hermitian lattices of rank $12$ over the Eisenstein integers. This set is the domain for a certain space of algebraic modular forms. We find a basis of Hecke eigenforms, and guess global…

In a previous paper (arXiv:math-ph/0604055) we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this note we…

We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…

We study the positivity properties of the curvature operator for holomorphic Hermitian vector bundles. We obtain new characterization of semi-positive curvature operators for $(n,q)$ and $(p,n)$-forms by L2-estimates. The characterization…

We give two congruence properties of Hermitian modular forms of degree 2 over $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. The one is a congruence criterion for Hermitian modular forms which is generalization of Sturm's theorem.…