Standard modules for tabular algebras

Details Standard modules for tabular algebras Standard modules for tabular algebras

2002-10-21

arxiv.org/abs/math/0210323v1

Mathematics

Quantum Algebra

Around 29 pages, AMSTeX

Scientific paper

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.

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