Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.Comment: Latex, 75 pages. Minor corrections. Final version, to appear in the Japanese Journal of Mathematic

Podocarpaceae in tropical forests: A synthesis

The Podocarpaceae comprises 18 genera and about 173 species of evergreen, coniferous trees and shrubs. It is the most successful gymnosperm family in angiosperm-dominated tropical forests (Brodribb, this volume). Podocarps are distributed mainly in the Southern Hemisphere, with populations also extending as far north as China and Japan and to Mexico and the Caribbean in the neotropics (Dalling et al., this volume; Enright and Jaffré, this volume; Adie and Lawes, this volume)