We study the eigenspace decomposition of a basic classical Lie superalgebra under the adjoint action of a toral subalgebra, thus extending results of Kostant. In recognition of Kostant's contribution we refer to the eigenfunctions appearing in the decomposition as Kostant roots. We then prove that Kostant root systems inherit the main properties of classical root systems. Our approach is combinatorial in nature and utilizes certain graphs naturally associated with Kostant root systems. In particular, we reprove Kostant's results without making use of the Killing form.
On Kostant root systems of Lie superalgebras / Dimitrov I.; Fioresi R.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 570:(2021), pp. 678-701. [10.1016/j.jalgebra.2020.11.015]
On Kostant root systems of Lie superalgebras
Dimitrov I.;Fioresi R.
2021
Abstract
We study the eigenspace decomposition of a basic classical Lie superalgebra under the adjoint action of a toral subalgebra, thus extending results of Kostant. In recognition of Kostant's contribution we refer to the eigenfunctions appearing in the decomposition as Kostant roots. We then prove that Kostant root systems inherit the main properties of classical root systems. Our approach is combinatorial in nature and utilizes certain graphs naturally associated with Kostant root systems. In particular, we reprove Kostant's results without making use of the Killing form.File | Dimensione | Formato | |
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