caa a22 4500 475738268 CHVBK 20180406123452.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/s002220050371 doi (NATIONALLICENCE)springer-10.1007/s002220050371 Ginzburg Victor The University of Chicago, Mathematics Department, Chicago, IL 60637, USA¶(e-mail: ginzburg@math.uchicago.edu), US aut Principal nilpotent pairs in a semisimple Lie algebra 1 [Elektronische Daten] [Victor Ginzburg] Abstract. : 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. 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 ?? 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. First results towards a complete classification of all principal nilpotent pairs in a simple Lie algebra are presented at the end of this paper in an Appendix, written by A. Elashvili and D. Panyushev. Springer-Verlag Berlin Heidelberg, 2000 https://doi.org/10.1007/s002220050371 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220050371 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ginzburg Victor The University of Chicago, Mathematics Department, Chicago, IL 60637, USA¶(e-mail: ginzburg@math.uchicago.edu), US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer