Boundary maps and maximal representations on infinite-dimensional Hermitian symmetric spaces

We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite-dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type, we show that there cannot be Zariski-dense maximal representations, and whenever the existence of a boundary map can be guaranteed, the representation preserves a finite-dimensional totally geodesic subspace on which the action is maximal. In the opposite direction, we construct examples of geometrically dense maximal representation in the infinite-dimensional Hermitian symmetric space of tube type and finite rank. Our approach is based on the study of boundary maps, which we are able to construct in low ranks or under some suitable Zariski density assumption, circumventing the lack of local compactness in the infinite-dimensional setting.

One Orthography, Four Lects: The Unified Berawan Orthography

Berawan is an endangered Austronesian language family consisting of four lects, which are Batu Belah, Long Teru, Long Jegan, and Long Terawan. Their settlements are located in the Malaysian state of Sarawak. The impetus for a unified orthography came from the Berawan community, who desire to write their lects consistently and reflecting the way they speak. The unified orthography was developed starting with a phonological analysis of the Berawan lects. This was followed by several orthography workshops and discussions with individual Berawan communities, culminating in a combined orthography workshop in which a unified orthography was agreed upon. The aim of the paper is to provide the groundwork for establishing the unifed orthography of the Berawan language family. A phonological comparison of the four Berawan varieties is included for this purpose. The phonological descriptions are taken from Burkhardt (2014). Smalley’s (1959, 1965) maxim of ‘maximal representation of speech’ and Rogers’s (2005) ‘shallow orthography’ approach are employed. On this basis, issues that arise for graphemic representation of Berawan phonemes are then discussed and the decisions made by the participants of the combined workshops are described. The paper also touches on issues encountered throughout the discussion. The issues that arose are primarily related to the differences in orthographic systems between the Berawan lects and the Malay language. The paper ends with a proposed unified Berawan orthography