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INVOLUTION MODELS OF FINITE COXETER GROUPS

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The document discusses the existence of involution models for finite Coxeter groups, establishing that a finite Coxeter group G has an involution model if and only if all its irreducible factors are of specific types (An, Bn, D2n+1, H3, or I2(n)). It explores various cases including dihedral groups and non-crystallographic groups, providing proofs and results related to their representations. The paper concludes with applications to classify finite subgroups of GL(2, R) and GL(3, R) that possess involution models.

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