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- W2008081522 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. 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." @default.
- W2008081522 created "2016-06-24" @default.
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- W2008081522 date "2000-06-01" @default.
- W2008081522 modified "2023-09-25" @default.
- W2008081522 title "Principal nilpotent pairs in a semisimple Lie algebra 1" @default.
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- W2008081522 doi "https://doi.org/10.1007/s002220050371" @default.
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