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**1 - 4**of**4**### Polytopal subcomplexes and homology representations of Coxeter groups Coxeter groups Reflections Polytopes Action on the half cube Homology representations

, 2011

"... Definition A Coxeter system is a pair (W,S), where W is a group given by the presentation 〈S | (si sj)mij = 1〉, where mij ∈ Z ∪ {∞} and we have mii = 1 and mij = mji. (If mij =∞, we omit the corresponding relation.) The group W above is known as a Coxeter group. It follows easily from the definition ..."

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Definition A Coxeter system is a pair (W,S), where W is a group given by the presentation 〈S | (si sj)mij = 1〉, where mij ∈ Z ∪ {∞} and we have mii = 1 and mij = mji. (If mij =∞, we omit the corresponding relation.) The group W above is known as a Coxeter group. It follows easily from the definition that the generators s have order 2. It is also true, but not obvious, that mij is the order of the product si sj. R.M. Green CU Boulder Polytopal subcomplexes and homology representations of Coxeter groups Coxeter groups Reflections Polytopes Action on the half cube Homology representations

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"... Quantum Groups Collective, a series of seminars involving universities in the north ..."

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Quantum Groups Collective, a series of seminars involving universities in the north