Related papers: Computational Modular Character Theory
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…
Neural network approaches have been applied to computational morphology with great success, improving the performance of most tasks by a large margin and providing new perspectives for modeling. This paper starts with a brief introduction…
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary…
This article presents a methodology that automatically derives a combinatorial specification for a permutation class C, given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is…
We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the…
Motivic local systems over a curve in finite characteristic form a countable set endowed with an action of the absolute Galois group of rational numbers commuting with the Frobenius map. I will discuss three series of conjectures about such…
Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of…
This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1.…
In this paper, we extend the Topological Quantum Field Theory developed by Gonz\'alez-Prieto, Logares, and Mu\~noz for computing virtual classes of $G$-representation varieties of closed orientable surfaces in the Grothendieck ring of…
The notion of the supercharacter theory was introduced by P.Diaconis and I.M.Isaaks in 2008. In this paper we review the main statements of the general theory, we observe the construction of supercharacter theory for algebra groups and the…
This paper constructs a combinatorial model for all postcritically finite rational maps arising as the Newton's method of a complex polynomial. This model is used in [LMS] to give a combinatorial classification of postcritically finite…
Motivic characteristic classes of possibly singular algebraic varieties are homology class versions of motivic characteristics, not classes in the so-called motivic (co)homology. This paper is a survey on them with more emphasis on…
This dissertation gives an overview of Martin Lof's dependant type theory, focusing on its computational content and addressing a question of possibility of fully canonical and computable semantic presentation.
We study modular ortholattices in the variety generated by the finite dimensional ones from an equational and geometric point of view. We relate this to coordinatization results.
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…
We discuss various computational issues around the problem of determining the character values of finite Chevalley groups, in the framework provided by Lusztig's theory of character sheaves. Some of the remaining open questions (concerning…
In computable analysis, sequences of rational numbers which effectively converge to a real number x are used as the (rho-) names of x. A real number x is computable if it has a computable name, and a real function f is computable if there…
The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
A minimal model of polychronous groups in neural networks is presented. The model is computationally efficient and allows the study of polychronous groups independent of specific neuron models. Computational experiments were performed with…