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Standard modules for tabular algebras

R. M. Green
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Abstract

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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R. M. Green. 2002-10-21. Standard modules for tabular algebras. https://arxiv.org/abs/math/0210323

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