Affine twisted length function

2021/05/25 by Chapelier-Laget, Nathan
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.12255

Abstract

Let W_a be an affine Weyl group. In 1987 Jian Yi Shi gave a characterization of the elements w ∈ W_a in terms of Φ⁺-tuples (k(w,α))_{α∈ Φ⁺} called the Shi vectors. Using these coefficients, a formula is provided to compute the standard length of W_a. In this note we express the twisted affine length function of W_a in terms of the Shi coefficients.

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