Commuting charges and symmetric spaces

Commuting charges and symmetric spaces

Every classical sigma-model with target space a compact symmetric space G/H (with G classical) is shown to possess infinitely many local, commuting, conserved charges which can be written in closed form. The spins of these charges run over a characteristic set of values, playing the role of exponents of G/H, and repeating modulo an integer h which plays the role of a Coxeter number.

Generalized Symmetric Berwald Spaces

In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.

Invariant and Coinvariant Spaces for the Algebra of Symmetric Polynomials in Non-Commuting Variables

We analyze the structure of the algebra K〈x〉n of symmetric polynomials in non-commuting variables in so far as it relates to K[x]n , its commutative counterpart. Using the “place-action” of the symmetric group, we are able to realize the latter as the invariant polynomials inside the former. We discover a tensor product decomposition of K〈x〉n analogous to the classical theorems of Chevalley, Sh...

Algebraic Groups with a Commuting Pair of Involutions and Semisimple Symmetric Spaces

Let G be a connected reductive algebraic group defined over an algebraically closed field F of characteristic not 2. Denote the Lie algebra of G by 9. In this paper we shall classify the isomorphism classes of ordered pairs of commuting involutorial automorphisms of G. This is shown to be independent of the characteristic of F and can be applied to describe all semisimple locally symmetric spac...

Commuting pairs of patterns and symmetric realizations