Ramified partition algebras
Abstract
Description
We introduce the ramified partition algebra, which is a physically motivated and natural generalization of the partition algebra. We investigate its representation theory and demonstrate quasi--heredity under certain conditions. Under these conditions we determine an index set for simple modules and construct standard modules with this index set.
We construct tensor space representations of certain non--semisimple specializations, and show how to use these to build clock model transfer matrices in arbitrary physical dimensions.
26 pages, multiple figures (eepic), latex, 1 figure has "too many points" for xdvi (but not gv)
26 pages, multiple figures (eepic), latex, 1 figure has "too many points" for xdvi (but not gv)