91,081 research outputs found
The development version of the CHEVIE package of GAP3
I describe the current state of the development version of the CHEVIE
package, which deals with Coxeter groups, reductive algebraic groups, complex
reflection groups, Hecke algebras, braid monoids, etc... Examples are given,
showing the code to check some results of Lusztig.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1003.492
"Case-free" derivation for Weyl groups of the number of reflection factorisations of a Coxeter element
Chapuy and Stump have given a nice generating series for the number of
factorisations of a Coxeter element as a product of reflections. Their method
is to evaluate case by case a character-theoretic expression. The goal of this
note is to give a uniform evaluation of their character-theoretic expression in
the case of Weyl groups, by using combinatorial properties of Deligne-Lusztig
representations.Comment: 5 page
Hurwitz action on tuples of Euclidean reflections
We show that if a tuple of Euclidean reflections has a finite orbit under the
Hurwitz action of the Artin braid group, then the group generated by these
reflections is finite. Humphries has published a similar statement but his
proof is irremediably flawed. At the same time as correcting his proof, our
proof is much simpler that Dubrovin and Mazocco's proof for triples of
reflections.Comment: redige le 1-9-200
Current challenges in finance : New theoretical approaches in financial and banking risk management
Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb systems. III Loopwise Expansion
We present an exact field theoretical representation of an ionic solution
made of charged hard spheres. The action of the field theory is obtained by
performing a Hubbard-Stratonovich transform of the configurational Boltzmann
factor. It is shown that the Stillinger-Lovett sum rules are satisfied if and
only if all the field correlation functions are short range functions. The mean
field, Gaussian and two-loops approximations of the theory are derived and
discussed. The mean field approximation for the free energy constitutes a
rigorous lower bound for the exact free energy, while the mean field pressure
is an upper bound. The one-loop order approximation is shown to be identical
with the random phase approximation of the theory of liquids. Finally, at the
two-loop order and in the pecular case of the restricted primitive model, one
recovers results obtained in the framework of the mode expansion theory.Comment: 35 pages, 3 figure
Quantum Mechanics Unscrambled
Is quantum mechanics about 'states'? Or is it basically another kind of
probability theory? It is argued that the elementary formalism of quantum
mechanics operates as a well-justified alternative to 'classical'
instantiations of a probability calculus. Its providing a general framework for
prediction accounts for its distinctive traits, which one should be careful not
to mistake for reflections of any strange ontology. The suggestion is also made
that quantum theory unwittingly emerged, in Schroedinger's formulation, as a
'lossy' by-product of a quantum-mechanical variant of the Hamilton-Jacobi
equation. As it turns out, the effectiveness of quantum theory qua predictive
algorithm makes up for the computational impracticability of that master
equation.Comment: 25 pages, no figures, final versio
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