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A q-Analog of the Coxeter Complex

โœ Scribed by A. Mathas

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
739 KB
Volume
164
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

In this paper a (q)-analogue of the Coxeter complex of a finite Coxeter group (W) is constructed for the (generic) Hecke algebra (\mathscr{H}) associated to (W). It is shown that the homology of this chain complex, together with that of its truncations, vanishes away from top dimension. The remainder of the paper investigates the representations of (\mathscr{H}) afforded by the top homology modules of these complexes. In particular necessary and sufficient conditions are given for a specialisation of the Hecke algebra to decompose into a direct sum of its "truncation" representations. 1994 Academic Press, Inc.

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For 0 < q < 1 define the symmetric q-linear operator acting on a suitable function f(x) by df(x)=f(q 1/2 x) -f(q -1/2 x). The q-linear initial value problem df(x) dx = lf(x), f(0)=1, has two entire functions C q (z) and S q (z) as linearly independent solutions. The functions C q (z) and S q (z) are