2008/03/06 by Meinolf Geck, Geck, Meinolf
Mathematics · #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.0803.0842
openalex publication_date 2008/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \bH be the generic Iwahori--Hecke algebra associated with a finite Coxeter group W. Recently, we have shown that \bH admits a natural cellular basis in the sense of Graham--Lehrer, provided that W is a Weyl group and all parameters of \bH are equal. The construction involves some data arising from the Kazhdan--Lusztig basis \\bCw\ of \bH and Lusztig's asymptotic ring \bJ. This article attemps to study \bJ and its representation theory from a new point of view. We show that \bJ can be obtained in an entirely different fashion from the generic representations of \bH, without any reference to \\bCw\. Then we can extend the construction of the cellular basis to the case where W is not crystallographic. Furthermore, if \bH is a multi-parameter algebra, we will see that there always exists at least one cellular structure on \bH. Finally, one may also hope that the new construction of \bJ can be extended to Hecke algebras associated to complex reflection groups.