On Kostant root systems of Lie superalgebras
| Autor: | Ivan Dimitrov, Rita Fioresi |
|---|---|
| Přispěvatelé: | Dimitrov I., Fioresi R. |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Parabolic subalgebra 010102 general mathematics Subalgebra Lie superalgebra Root system Eigenfunction Killing form Eigenspace decomposition 01 natural sciences Action (physics) Simple roots Mathematics::Quantum Algebra 0103 physical sciences Kostant root system Hermitian symmetric pair 010307 mathematical physics 0101 mathematics Mathematics::Representation Theory Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Journal of Algebra. 570:678-701 |
| ISSN: | 0021-8693 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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