625 research outputs found
Primitive Monodromy Groups of Genus at most Two
We show that if the action of a classical group on a set of
-spaces of its natural module is of genus at most two, then
Rank 3 permutation characters and maximal subgroups
In this paper we classify all maximal subgroups M of a nearly simple
primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit
E of non-singular points of the natural module for L such that 1_P^G <=1_M^G
where P is a stabilizer of a point in E. This result has an application to the
study of minimal genera of algebraic curves which admit group actions.Comment: 41 pages, to appear in Forum Mathematicu
Birational properties of some moduli spaces related to tetragonal curves of genus 7
Let M_{7,n} be the (coarse) moduli space of smooth curves of genus 7 with n
marked points defined over the complex field. We denote by M^1_{7,n;4} the
locus of points inside M_{7,n} representing curves carrying a g^1_4. It is
classically known that M^1_{7,n;4} is irreducible of dimension 17+n. We prove
in this paper that M^1_{7,n;4} is rational for 0<= n <= 11.Comment: 20 pages; in the second version we replaced the previous Lemma 4.3 by
Lemma 4.5, and fixed the proof of the rationality of the moduli space of
unpointed tetragonal genus 7 curves in section 4. Hans-Christian von Bothmer
as further author adde
Fusion rules in conformal field theory
Several aspects of fusion rings and fusion rule algebras, and of their
manifestations in twodimensional (conformal) field theory, are described:
diagonalization and the connection with modular invariance; the presentation in
terms of quotients of polynomial rings; fusion graphs; various strategies that
allow for a partial classification; and the role of the fusion rules in the
conformal bootstrap programme.Comment: 68 pages, LaTeX. changed contents of footnote no.
Free Probability Theory
Free probability theory is a line of research which parallels aspects of classical probability, in a non-commutative context where tensor products are replaced by free products, and independent random variables are replaced by free random variables. The theory grew out of attempts to solve some longstanding problems about von Neumann algebras of free groups. In the almost twenty years since its creation, free probability has become a subject in its own right, with connections to several other parts of mathematics: operator algebras, the theory of random matrices, classical probability and the theory of large deviations, algebraic combinatorics, topology. Free probability also has connections with applied mathematics (wireless communication) and some mathematical models in theoretical physics. The Oberwolfach workshop on free probability brought together a very strong group of mathematicians representing the current directions of development in the area
Hearing shapes of drums - mathematical and physical aspects of isospectrality
In a celebrated paper '"Can one hear the shape of a drum?"' M. Kac [Amer.
Math. Monthly 73, 1 (1966)] asked his famous question about the existence of
nonisometric billiards having the same spectrum of the Laplacian. This question
was eventually answered positively in 1992 by the construction of noncongruent
planar isospectral pairs. This review highlights mathematical and physical
aspects of isospectrality.Comment: 42 pages, 60 figure
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