Related papers: Drinfeld modules in SageMath
We formulate sufficient conditions for the strong integrability of dressing cosets. We provide several sigma-model backgrounds solving those conditions, some of them are new and some of them were not so far formulated as the dressing…
We introduce FlagAlgebraToolbox, an extension of SageMath capable of automating flag algebra calculations and optimizations. FlagAlgebraToolbox has a simple interface, can handle a wide range of combinatorial theories, can numerically…
Drinfeld orbifold algebras are a type of deformation of skew group algebras generalizing graded Hecke algebras of interest in representation theory, algebraic combinatorics, and noncommutative geometry. In this article, we classify all…
In this paper, we prove explicit reciprocity laws for a class of formal Drinfeld modules having stable reduction of height one, in the spirit of those existing in characteristic zero (cf. the work of Wiles). We begin by defining the Kummer…
We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with…
I introduce new Langlands duality conjectures concerning skein modules of 3-manifolds, which we have made recently with David Ben-Zvi, Sam Gunningham, and Pavel Safronov. I recount some historical motivation and some recent special cases…
We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper…
SModelS is an automatised tool for the interpretation of simplified model results from the LHC. It allows to decompose models of new physics obeying a Z2 symmetry into simplified model components, and to compare these against a large…
Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. This way, Durgun has introduced absolutely pure domains of modules as a mean…
In this article, we give an explicit description of the invertible functions on the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. We identify them with some distribution spaces over the profinite set of…
We present our effort to extend and complement the core modules of the Distributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key…
In this article we give a Drinfeld modular interpretation for various towers of function fields meeting Zink's bound.
In that paper, we recall the notion of the multidegree for $D$-modules, as exposed in a previous paper, with a slight simplification. A particular emphasis is given on hypergeometric systems, used to provide interesting and computable…
Let $\mathbb{F}_q$ be the field of $q$ elements and let $A=\mathbb{F}_q[t]$ be the polynomial ring over $\mathbb{F}_q$. Let $\mathfrak{n}\in A\setminus \mathbb{F}_q$ be a monic polynomial with a prime factor of degree prime to $q-1$. Let…
This note summarizes the talk by the author at the workshop "Geometry and Computer Science" held in Pescara in February 2017. We present how SageMath can help in research in Complex and Differential Geometry, with two simple applications,…
We rederive a popular nonsemisimple fusion algebra in the braided context, from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant…
We present the first public release of ShapePipe, an open-source and modular weak-lensing measurement, analysis, and validation pipeline written in Python. We describe the design of the software and justify the choices made. We provide a…
Fix an affine Lie algebra $\widehat{\mathfrak{g}}_\kappa$ with associated principal affine W-algebra $\mathcal{W}_\kappa$. A basic conjecture of Frenkel--Kac--Wakimoto asserts that Drinfeld--Sokolov reduction sends admissible…
We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly…
Let H be an infinite-dimensional Taft algebra over an algebraically closed field k of characteristic 0. We find all the simple Yetter-Drinfeld modules V over H, and classifies those V with B(V) is finite-dimensional.