Related papers: Classical conformal blocks

Let G be a simple classical algebraic group over an algebraically closed field of positive characteristic. We describe the support variety of a simple G-module over the r-th Frobenius kernel of G, in terms of its calculation over the first…

In this article we present an efficient algorithm to compute rotation intervals of circle maps of degree one. It is based on the computation of the rotation number of a monotone circle map of degree one with a constant section. The main…

A unified construction of high order shape functions is given for all four classical energy spaces ($H^1$, $H(\mathrm{curl})$, $H(\mathrm{div})$ and $L^2$) and for elements of "all" shapes (segment, quadrilateral, triangle, hexahedron,…

We give a complete classification of edge-to-edge tilings of the sphere by regular polygons under a unified framework. Without assuming convexity of the tiles or polyhedrality of the underlying graph, our proof is independent of the…

We describe a framework to construct tropical moduli spaces of rational stable maps to a smooth tropical hypersurface or curve. These moduli spaces will be tropical cycles of the expected dimension, corresponding to virtual fundamental…

We give combinatorial formulas for F-polynomials in cluster algebras of classical types in terms of the weighted paths in certain directed graphs. As a consequence we prove the positivity of F-polynomials in cluster algebras of classical…

We study the space of deformations of a smooth foliation of the 5-sphere by complex manifolds

We use classical invariant theory to solve the biholomorphic equivalence problem for two families of plane curve singularities previously considered in the literature. Our calculations motivate an intriguing conjecture that proposes a way…

In this paper, we compute the cohomology of the Heisenberg-Virasoro conformal algebra with coefficients in its modules, and in particular with trivial coefficients both for the basic and reduced complexes.

Generalizing the octahedral configuration of six congruent cylinders touching the unit sphere, we exhibit configurations of congruent cylinders associated to a pair of dual Platonic bodies.

We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.

We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…

In this note, we will consider two classical volume problems related to elliptic integrals. The first problem has a neat formula by means of elliptic integrals. We remade it with details. In the second problem, we found a messy formula. On…

Let T be a maximal torus in a classical linear group G. In this paper we find all simple rational G-modules V such that for each vector v in V the closure of its T-orbit is a normal affine variety. For every other G-module we present a…

We describe the constructible derived category of sheaves on the $n$-sphere, stratified in a point and its complement, as a dg module category of a formal dg algebra. We prove formality by exploring two different methods: As a combinatorial…

We classify the dihedral edge-to-edge tilings of the sphere by squares and rhombi.

We apply an integral transformation to solutions of a partial differential equation for five-point correlation functions in Liouville theory on a sphere with one degenerate field $V_{-\frac{1}{2b}}$. By repeating this transformation, we can…

In this article, we first give a short introduction to conformal algebras. Then we present three families of simple conformal algebras finite growth generated by simple Jordan algebras of types A, B, C.

The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…

This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and…