Remarks on Decompositions of the Longest Element of the Weyl Group
摘要
The longest element of any finite Weyl group W decomposes into a product of several reflections corresponding to the so-called max-orthogonal subset of roots. This decomposition is unique. Factors for such decomposition are listed for each type of root system. The set of the roots of the max-orthogonal decomposition coincides with Kostant’s cascade of orthogonal roots constructed for calculations in the universal enveloping algebra.