We define for any crystallographic root system a new statistic on the corresponding Weyl group which we call the odd length. This statistic reduces, for Weyl groups of types A, B, and D, to each of the statistics by the same name that have already been defined and studied in the literature. We show that the sign-twisted generating function of the odd length always factors completely, and we obtain multivariate analogues of these factorizations in types B and D.
Brenti, F., Carnevale, A. (2019). Odd length in Weyl groups. ALGEBRAIC COMBINATORICS, 2(6), 1125-1147 [10.5802/alco.69].
Odd length in Weyl groups
Francesco Brenti
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2019-01-01
Abstract
We define for any crystallographic root system a new statistic on the corresponding Weyl group which we call the odd length. This statistic reduces, for Weyl groups of types A, B, and D, to each of the statistics by the same name that have already been defined and studied in the literature. We show that the sign-twisted generating function of the odd length always factors completely, and we obtain multivariate analogues of these factorizations in types B and D.File in questo prodotto:
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