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Hilbert-Poincare series for spaces of commuting elements in Lie groups
In this article we study the homology of spaces
of ordered pairwise commuting -tuples in a Lie group . We give an
explicit formula for the Poincare series of these spaces in terms of invariants
of the Weyl group of . By work of Bergeron and Silberman, our results also
apply to , where the subgroups are
the terms in the descending central series of the free group . Finally, we
show that there is a stable equivalence between the space
studied by Cohen-Stafa and its nilpotent analogues.Comment: 20 pages, journal versio
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