Mathematics – Representation Theory
Scientific paper
1999-03-10
Mathematics
Representation Theory
new section on Partial Slices added; minor corrections made; 46 pp., AMS-TeX, 1 eps figure
Scientific paper
10.1007/s002220050371
This is the first of a series of papers devoted to certain pairs of commuting nilpotent elements in a semisimple Lie algebra that enjoy quite remarkable properties and which are expected to play a major role in Representation theory. The properties of these pairs and their role is similar to those of the principal nilpotents. To any principal nilpotent pair we associate a two-parameter analogue of the Kostant partition function, and propose the corresponding two-parameter analogue of the weight multiplicity formula. In a different direction, each principal nilpotent pair gives rise to a harmonic polynomial on the Cartesian square of the Cartan subalgebra, that transforms under an irreducible representation of the Weyl group. In the special case of sl_n, the conjugacy classes of principal nilpotent pairs and the irreducible representations of the Symmetric group, S_n, are both parametrised (in a compatible way) by Young diagrams. In general, our theory provides a natural generalization to arbitrary Weyl groups of the classical construction of simple S_n-modules in terms of Young's symmetrisers.
Ginzburg Victor
No associations
LandOfFree
Principal Nilpotent pairs in a semisimple Lie algebra, I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Principal Nilpotent pairs in a semisimple Lie algebra, I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Principal Nilpotent pairs in a semisimple Lie algebra, I will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-267542