22,050 research outputs found
Recursive Representations of Arbitrary Virasoro Conformal Blocks
We derive recursive representations in the internal weights of N-point
Virasoro conformal blocks in the sphere linear channel and the torus necklace
channel, and recursive representations in the central charge of arbitrary
Virasoro conformal blocks on the sphere, the torus, and higher genus Riemann
surfaces in the plumbing frame.Comment: 39 pages, 8 figures, v2: comments on references added, reference
added, typos corrected, v3: comments on the relation between the plumbing and
the Schottky parameters added, v4: typos correcte
Reflection groups and polytopes over finite fields, II
When the standard representation of a crystallographic Coxeter group
is reduced modulo an odd prime , a finite representation in some orthogonal
space over is obtained. If has a string diagram, the
latter group will often be the automorphism group of a finite regular polytope.
In Part I we described the basics of this construction and enumerated the
polytopes associated with the groups of rank 3 and the groups of spherical or
Euclidean type. In this paper, we investigate such families of polytopes for
more general choices of , including all groups of rank 4. In
particular, we study in depth the interplay between their geometric properties
and the algebraic structure of the corresponding finite orthogonal group.Comment: 30 pages (Advances in Applied Mathematics, to appear
Regular maps of high density
A regular map is a surface together with an embedded graph, having properties
similar to those of the surface and graph of a platonic solid. We analyze
regular maps with reflection symmetry and a graph of density strictly exceeding
1/2, and we conclude that all regular maps of this type belong to a family of
maps naturally defined on the Fermat curves x^n+y^n+z^n=0, excepting the one
corresponding to the tetrahedron.Comment: 13 pages, 4 figure
Problems on Polytopes, Their Groups, and Realizations
The paper gives a collection of open problems on abstract polytopes that were
either presented at the Polytopes Day in Calgary or motivated by discussions at
the preceding Workshop on Convex and Abstract Polytopes at the Banff
International Research Station in May 2005.Comment: 25 pages (Periodica Mathematica Hungarica, Special Issue on Discrete
Geometry, to appear
Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
We compute the generating functions of a O(n) model (loop gas model) on a
random lattice of any topology. On the disc and the cylinder, they were already
known, and here we compute all the other topologies. We find that the
generating functions (and the correlation functions of the lattice) obey the
topological recursion, as usual in matrix models, i.e they are given by the
symplectic invariants of their spectral curve.Comment: pdflatex, 89 pages, 12 labelled figures (15 figures at all), minor
correction
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