The effective action of N=2 Yang-Mills theory with adjoint matter is shown to be governed by an integrable spin model with spectral parameter on an elliptic curve. We sketch a route to deriving this effective dynamics from the underlying Yang-Mills theory. Natural generalizations of this structure to all N=2 models, and to string theory, are suggested.

This is a survey of results on self-adjoint commuting ordinary differential operators of rank two. In particular, the action of automorphisms of the first Weyl algebra on the set of commuting differential operators with polynomial coefficients is discussed, as well as the problem of constructing algebro-geometric solutions of rank l > 1 of soliton equations. Bibliography: 59 titles.

We construct generic Picard-Vessiot extensions for linear algebraic groups which are isomorphic to the semidirect product of a connected group G by an arbitrary finite group H, where the adjoint H-action on the Lie algebra of G is faithful.

In this paper, we consider the diagonal action of a connected semisimple group of adjoint type on its wonderful compactification. We show that the semistable locus is a union of the G-stable pieces and we calculate the geometric quotient. 0.

FOLLOING OUR PREVIOS PROJECT [1], WE ARE GOING TO PROVE THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE SPECTRAL PROBLEM IN THIS PROJECT.FIRST,WE HAVE PROVEN THE UNIQUENESS OF THE SOLUTION THEN TO PROVE THE EXISTRNCE WE CONSTENSS OF THE ADJOINT PROBLEM CORRESPONDING TO THIS SPECTRAL PROBLEM NEXT THE UNIQUESS OF THE ADJOINT PROBLEM IS THE EXISTENCE OF THE MAIN PROBLEM AS DISCUSSED BY[2] AND ...

We introduce and study a class of determinantal probability measures generalising the discrete point processes. These live on Grassmannian real, complex, or quaternionic inner product space that is split into pairwise orthogonal finite-dimensional subspaces. They are determined by positive self-adjoint contraction space, in way equivariant under action group isometries preserve splitting.

Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modiied, also on even-dimensional spaces, to make it equivariant with respect to the action of that group when the twisted adjoint representation is used in the deeni...