On the Kazhdan-Lusztig basis of a spherical Hecke algebra

Friedrich Knop

On the Kazhdan-Lusztig basis of a spherical Hecke algebra

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arxiv math/0403066 v2 pith:PVXAPPUH submitted 2004-03-03 math.RT math.QA

Friedrich Knop This is my paper · ORCID

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keywords algebrabasisheckekazhdan-lusztiglusztigsphericalcasecharacters

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Lusztig proved that the Kazhdan-Lusztig basis of a spherical Hecke algebra can be essentially identified with the Weyl characters of the Langlands dual group. We generalize this result to the unequal parameter case. The new proof is pretty simple and quite different from Lusztig's.

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In affine Hecke categories, high tensor powers of a fixed object have a number of indecomposable summands of order n^{-|Phi^+|/2} times an exponential; proved in type A1, and for longest elements in type A2, with coar...

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