2006/01/19 by Sankaran Viswanath, Viswanath, Sankaran
Computer Science · Mathematics · #20F55 #Advanced Graph Theory Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0601482
openalex publication_date 2006/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The principal objects studied in this note are Coxeter groups W that are neither finite nor affine. A well known result of de la Harpe asserts that such groups have exponential growth. We consider quotients of W by its parabolic subgroups and by a certain class of reflection subgroups. We show that these quotients have exponential growth as well. To achieve this, we use a theorem of Dyer to construct a reflection subgroup of W that is isomorphic to the universal Coxeter group on three generators. The results are all proved under the restriction that the Coxeter diagram of W is simply laced, and some remarks made on how this restriction may be relaxed.