1,452 research outputs found
Hecke algebras of finite type are cellular
Let \cH be the one-parameter Hecke algebra associated to a finite Weyl
group , defined over a ground ring in which ``bad'' primes for are
invertible. Using deep properties of the Kazhdan--Lusztig basis of \cH and
Lusztig's \ba-function, we show that \cH has a natural cellular structure
in the sense of Graham and Lehrer. Thus, we obtain a general theory of ``Specht
modules'' for Hecke algebras of finite type. Previously, a general cellular
structure was only known to exist in types and .Comment: 14 pages; added reference
Eigenvalues of real symmetric matrices
We present a proof of the existence of real eigenvalues of real symmetric
matrices which does not rely on any limit or compactness arguments, but only
uses the notions of "sup", "inf".Comment: 2 pages; appears in the Amer. Math. Monthly (2015
Computing Kazhdan--Lusztig cells for unequal parameters
Following Lusztig, we consider a Coxeter group together with a weight
function . This gives rise to the pre-order relation and the
corresponding partition of into left cells. We introduce an equivalence
relation on weight functions such that, in particular, is constant
on equivalent classes. We shall work this out explicitly for of type
and check that several of Lusztig's conjectures concerning left cells with
unequal parameters hold in this case, even for those parameters which do not
admit a geometric interpretation. The proofs involve some explicit computations
using {\sf CHEVIE}
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