Trilobitenperlen from Dunaszekcső (Hungary)

In the Csanády-collection (Bátaszék, Hungary) there are two unpublished two-channelled glass beads. They had been found on the banks of the river Danube in Dunaszekcsô in Hungary by a fisherman and were presented to the Csanády-collection in or after 1965 (Mrs Csanády pers. comm.). These special beads are called Rippen-glasperlen (Noll 1963, 68) or Trilobitenperlen (Haevernick 1974, 105) in the literature. One can set up two main groups of Trilobitenperlen on the basis of decoration: 1. beads with figurative decoration, which are also called two-channelled glass cameos (Gesztelyi 1997) and 2. beads without figurative decoration. T. E. Haevernick, who set up a basic typology for the Trilobitenperlen further divided the non-figurative beads into Glatt-gerript type and Kariert-gerript type (Havevernick 1974, 106)

Standard Monomial Theory for Bott-Samelson Varieties of GL(n)

We construct an explicit basis for the coordinate ring of the Bott-Samelson variety Z_i associated to G = GL(n) and an arbitrary sequence of simple reflections i. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties. Our standard tableaux have a natural crystal graph structure.Comment: Northeastern University, [email protected] AMSTeX amspp

Generically transitive actions on multiple flag varieties

Let $G$ be a semisimple algebraic group whose decomposition into a product of simple components does not contain simple groups of type $A$, and $P\subseteq G$ be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples $(G, P, n)$ such that (a) there exists an open $G$-orbit on the multiple flag variety $G/P\times G/P\times\ldots\times G/P$ ($n$ factors), (b) the number of $G$-orbits on the multiple flag variety is finite.Comment: 10 page