***************************************************************************** * 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: St001148 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The dimension of the adjoint representation of the Lie group of given type. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(C): return WeylCharacterRing(C).adjoint_representation().degree() ----------------------------------------------------------------------------- Statistic values: ['A',1] => 3 ['A',2] => 8 ['B',2] => 10 ['G',2] => 14 ['A',3] => 15 ['B',3] => 21 ['C',3] => 21 ['A',4] => 24 ['B',4] => 36 ['C',4] => 36 ['D',4] => 28 ['F',4] => 52 ['A',5] => 35 ['B',5] => 55 ['C',5] => 55 ['D',5] => 45 ['A',6] => 48 ['B',6] => 78 ['C',6] => 78 ['D',6] => 66 ['E',6] => 78 ['A',7] => 63 ['B',7] => 105 ['C',7] => 105 ['D',7] => 91 ['E',7] => 133 ['A',8] => 80 ['B',8] => 136 ['C',8] => 136 ['D',8] => 120 ['E',8] => 248 ----------------------------------------------------------------------------- Created: Apr 19, 2018 at 10:24 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 19, 2018 at 10:24 by Martin Rubey