20 research outputs found
Hidden Symmetries of Stochastic Models
In the matrix product states approach to species diffusion processes the
stationary probability distribution is expressed as a matrix product state with
respect to a quadratic algebra determined by the dynamics of the process. The
quadratic algebra defines a noncommutative space with a quantum group
action as its symmetry. Boundary processes amount to the appearance of
parameter dependent linear terms in the algebraic relations and lead to a
reduction of the symmetry. We argue that the boundary operators of
the asymmetric simple exclusion process generate a tridiagonal algebra whose
irriducible representations are expressed in terms of the Askey-Wilson
polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary
problem and allows to solve the model exactly.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras
Deformed parabose and parafermi algebras are revised and endowed with Hopf
structure in a natural way.
The noncocommutative coproduct allows for construction of parastatistics
Fock-like representations, built out of the simplest deformed bose and fermi
representations. The construction gives rise to quadratic algebras of deformed
anomalous commutation relations which define the generalized Green ansatz.Comment: 14 pages, final versio