SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS

Involutions of compact Riemannian 4-symmetric spaces

Let G/H be a compact 4-symmetric space of inner type such that the dimension of the center Z(H) of H is at most one. In this paper we shall classify involutions of G preserving H for the case where dimZ(H) = 0, or H is a centralizer of a toral subgroup of G.

Graded Algebras, Anti-involutions, Simple Groups and Symmetric Spaces

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...

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.

Symmetric Schröder paths and restricted involutions

Let Ak be the set of permutations in the symmetric group Sk with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns Ak. We present a bijection between symmetric Schröder paths of length 2n and involutions of length n + 1 avoiding A4. Statistics such as the number of right-to-left maxima and fixed points of the involution correspond to the number of ste...