Papers › Braid relations for involution words in affine Coxeter groups
Braid relations for involution words in affine Coxeter groups
Eric Marberg
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We describe an algorithm to identify a minimal set of "braid relations" which span and preserve all sets of involution words for twisted Coxeter systems of finite or affine type. We classify the cases in which adding the smallest possible set of "half-braid" relations to the ordinary braid relations produces a spanning set: in the untwisted case, this occurs for the Coxeter systems which are finite with rank two or type Aₙ, or affine with rank three or type Ãₙ. These results generalize recent work of Hu and Zhang on the finite classical cases.
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