On symmetric invariants of centralisers in reductive Lie algebras
By Dmitri I. Panyushev, A. Premet, Oksana Yakimova. 2006
89 citations recorded by the source corpus.
Let g be a finite-dimensional simple Lie algebra of rank l over an algebraically closed field of characteristic 0. Let e be a nilpotent element of g and let ge be the centraliser of e in g. In this paper we study the algebra S(ge)ge of symmetric invariants of ge. We prove that if g is of type A or C, then S(ge)ge is always a graded polynomial algebra in l variables, and we show that this continues to hold for some nilpotent elements in the Lie algebras of other types. In type A we prove that the invariant algebra S(ge)ge is freely generated by a regular sequence in S(ge) and describe the tangent cone at e to the nilpotent variety of g.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5f1be0c39fa1377aebeb4ed14bf7cd8e80f91c33
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In Algebra and Number Theory
- Doron Shafrir
- Anthony Joseph
- Oksana Yakimova
- Dmitri I. Panyushev
- Paul Blain Levy
- Mark Reeder
- E. Sommers
In Geometry and Topology
- Doron Shafrir
- Anthony Joseph
- Oksana Yakimova
- Dmitri I. Panyushev
- Paul Blain Levy
- Mark Reeder
- E. Sommers
In Mathematical Physics
Citations in the corpus
- The argument shift method and maximal commutative subalgebras of Poisson algebras (2007, background): “is an open subset of q whose complement is of codimension > 2. This means, in turn, that [ 9, Theorem 1.1 ] applies to the polynomial subalgebra F S (q).”
- Polynomiality of invariants, unimodularity and adapted pairs (2010, background): “(Since they apply the weaker version [ 31, Theorem 1.2 ] of Lemma 5.4, they just do this in the case when a is nonsingular.) In any case the technically dicult part is to nd enough low degree elements of Y (a).”