536 research outputs found
Quasiinvariants of Coxeter groups and m-harmonic polynomials
The space of m-harmonic polynomials related to a Coxeter group G and a
multiplicity function m on its root system is defined as the joint kernel of
the properly gauged invariant integrals of the corresponding generalised
quantum Calogero-Moser problem. The relation between this space and the ring of
all quantum integrals of this system (which is isomorphic to the ring of
corresponding quasiinvariants) is investigated.Comment: 23 page
Canonically conjugate variables for the periodic Camassa-Holm equation
The Camassa-Holm shallow water equation is known to be Hamiltonian with
respect to two compatible Poisson brackets. A set of conjugate variables is
constructed for both brackets using spectral theory.Comment: 10 pages, no figures, LaTeX; v. 2,3: references updated, minor
change
Bernoulli numbers and solitons
We present a new formula for the Bernoulli numbers as the following integral
This formula is motivated by the
results of Fairlie and Veselov, who discovered the relation of Bernoulli
polynomials with soliton theory.Comment: 5 page
On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations
It is proved that if the Schr\"odinger equation of
Calogero-Moser-Sutherland type with
has a solution of the product form then the function satisfies the
generalised WDVV equations.Comment: 10 page
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