We show that the irregular connection on Gm constructed by Frenkel-Gross ([FG]) and the one constructed by Heinloth-Ngô-Yun ([HNY]) are the same, which confirms the Conjecture 2.14 of [HNY]. The proof is simple, modulo the big machinery of quantization of Hitchin’s integrable systems as developed by Beilinson-Drinfeld ([BD]). The idea is as follows. Let E be the irregular connection on Gm as co...

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi–Yau manifold. In physics such a function appears as the partition function of N = 2 superconformal field theories. In these notes we define the modified ...

We show how the weight of automorphic forms is related to the holomorphic positive and negative line bundles. Then, from the relation of holomorphic vector bundles and the existence of Yang-Mills connection on the stable bundle , we discuss how the weight of automorphic forms can be associated with the transition function of the Yang-Mills connection.

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations. c © 2006 Elsevier Ltd. All rights reserved.

Abstract After an overview of uses and explorations minimal automorphic ordered sets, we present a criterion when certain superpositions crowns are automorphic. A key lemma to exclude retracts can also be applied sets recently presented in Schröder (Order, https://doi.org/10.1007/s11083-021-09574-3 , 2021).

We characterize the space of the so-called planar mixed automorphic forms of type (ν, μ) with respect to an equivariant pair (ρ, τ) as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrödinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of...