Related papers: Characters and modular properties of permutation o…
We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.
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.
Boundary conformal field theory is the suitable framework for a microscopic treatment of D-branes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions…
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
Fermionic-type character formulae are presented for charged irreduciblemodules of the graded parafermionic conformal field theory associated to the coset $osp(1,2)_k/u(1)$. This is obtained by counting the weakly ordered `partitions'…
Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli…
The present paper is devoted to questions located at the junction of the theory of space quasiconformal mappings and Riemannian surfaces. Theorems on local behavior of one class of open discrete mappings with unbounded characteristic of…
Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…
We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.
We describe a birational map between subvarieties in the character varieties of mutative 3-manifolds. By studying the birational map, one can decide in certain circumstances whether a mutation surface is detected by an ideal point of the…
These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.
This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance…
We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of…
Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…
We introduce the concept of the modularity of an abelian variety defined over the rational number field extending the modularity of an elliptic curve. We discuss the modularity of an abelian variety over the rational number field. We…
Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their varied applications. For instance, in combinatorial design theory, a correspondence of perfect $c$-nonlinear…
We prove a broad generalization of a theorem of W. Burnside on real characters using permutation characters. Under a necessary hypothesis, We can give some control on multiplicities (a result that needs the Classification of Finite Simple…