Related papers: Computational Modular Character Theory
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
We compute the character tables of the following groups with character theoretic methods, using known information about the conjugacy classes and about the character tables of some subgroups and factor groups: $Th$, $J_4$, $2.{}^2E_6(2)$,…
Let S be a path-connected, locally-compact CW-complex, and let M be a subcomplex with finitely-many components. A `decorated SL_2(C)-local system' is an SL_2(C)-local system on S, together with a choice of `decoration' at each component of…
For a pivotal finite tensor category $\mathcal{C}$ over an algebraically closed field $k$, we define the algebra $\mathsf{CF}(\mathcal{C})$ of class functions and the internal character $\mathsf{ch}(X) \in \mathsf{CF}(\mathcal{C})$ for an…
We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a Polynomial On Residue Classes (PORC). The key…
We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
We describe an easy way how to find supercharacter theories for a finite group, if its character table is known. Namely, we show how an arbitrary partition of the conjugacy classes or of the irreducible characters can be refined to the…
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
Using computational methods, we complete the determination of the $3$-modular character table of the Chevalley group $F_4(2)$ and its covering group.
Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is…
We begin the systematic study of decision problems for finitely generated groups given by a solution to their word problem. We relate this to the study of computable analysis on the space of marked groups. We point out that several distinct…
Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
We show that the characters of tilting modules can be used, in a concrete and explicit way, to obtain the simple characters of a connected reductive algebraic group $G$ over an algebraically closed field $\Bbbk$ of characteristic $p$, for…
We develop a computational framework for the statistical characterization of Galois characters with finite image, with application to characterizing Galois groups and establishing equivalence of characters of finite images of…