Standard modules for tabular algebras

We introduce cell modules for the tabular algebras defined in a previous work (math.QA/0107230); these modules are analogous to the representations arising from left Kazhdan–Lusztig cells. The standard modules of the title are constructed in an elementary way by suitable tensoring of the cell modules. We show how a certain extended affine Hecke algebra of type $A$ equipped with its Kazhdan–Lusztig basis is an example of a tabular algebra, and verify that in this case our standard modules coincide with other standard modules defined in the literature.