***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000861 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The maximal dimension of an irreducible representation of the Weyl group of a finite Cartan type. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(cartan_type): W = ReflectionGroup(cartan_type) return max( chi(W.one()) for chi in W.irreducible_characters() ) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 2 ['B',2] => 2 ['G',2] => 2 ['A',3] => 3 ['B',3] => 3 ['C',3] => 3 ['A',4] => 6 ['B',4] => 8 ['C',4] => 8 ['D',4] => 8 ['F',4] => 16 ['A',5] => 16 ['B',5] => 20 ['C',5] => 20 ['D',5] => 20 ['A',6] => 35 ['B',6] => 80 ['C',6] => 80 ['D',6] => 45 ['E',6] => 90 ['A',7] => 90 ['B',7] => 210 ['C',7] => 210 ['D',7] => 210 ['E',7] => 512 ['A',8] => 216 ['B',8] => 672 ['C',8] => 672 ['D',8] => 672 ['E',8] => 7168 ----------------------------------------------------------------------------- Created: Jun 25, 2017 at 20:00 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Jun 25, 2017 at 20:00 by Christian Stump