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Zero excess and minimal length in finite coxeter groups
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Abstract
Let \mathcal{W} be the set of strongly real elements of W, a Coxeter group. Then for w∈W,
e(w), the excess of w, is defined by
e(w) = \min min \{l(x)+l(y) - l(w)| w = xy; x^2 = y^2 =1}. When W is finite we may also define E(w), the reflection excess of w. The main result established here is that if W is finite and X is a W-conjugacy class, then there
exists w∈X such that w has minimal length in X and e(w)=0=E(w)