We review the recent progress in the theoretical description and experimental observation of multiple parton interactions. Subjects covered include experimental measurements of minimum bias interactions and of the underlying event, models of soft phy
sics implemented in Monte Carlo generators, developments in the theoretical description of multiple parton interactions and phenomenological studies of double parton scattering. This article stems from contributions presented at the Helmholtz Alliance workshop on Multi-Parton Interactions at the LHC, DESY Hamburg, 13-15 September 2010.
We implement the Bethe anstaz method for the elliptic quantum group $E_{tau,eta}(A_2^{(2)})$. The Bethe creation operators are constructed as polynomials of the Lax matrix elements expressed through a recurrence relation. We also give the eigenvalues
of the family of commuting transfer matrices defined in the tensor product of fundamental representations.
