Let Sigma be the Davis complex for a Coxeter system (W,S). The automorphism group G of Sigma is naturally a locally compact group, and a simple combinatorial condition due to Haglund-Paulin determines when G is nondiscrete. The Coxeter group W may be regarded as a uniform lattice in G. We show that many such G also admit a uniform lattice Gamma, and an infinite family of nonuniform lattices with covolumes converging to that of Gamma. We also show that the nonuniform lattice Gamma is not finitely generated.
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After the seminar we will take the speaker to lunch.
See the Algebra Seminar web page for information about other seminars in the series.
James East jamese@maths.usyd.edu.au