Loading...
Please wait, while we are loading the content...
Similar Documents
The Symmetric Invariants of Centralizers and Finite W-algebras (組合せ論的表現論の展望 : Rims研究集会報告集)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Moreau, Anne |
| Copyright Year | 2015 |
| Abstract | Let g be a finite-dimensional simple Lie algebra of rank l over an algebraically closed field k of characteristic zero, and let e be a nilpotent element of g. Denote by g the centralizer of e in g and by S(g) e the algebra of symmetric invariants of g. We say that e is good if the nullvariety of some l homogeneous elements of S(g) e in (g) has codimension l. If e is good then S(g) e is polynomial. The main result of this paper stipulates that if for some homogeneous generators of S(g), the initial homogeneous component of their restrictions to e + g f are algebraically independent, with (e, h, f ) an sl2-triple of g, then e is good. The proof is strongly based on the theory of finite W-algebras. As applications, we pursue the investigations of [PPY07] and we produce (new) examples of nilpotent elements that verify the above polynomiality condition in simple Lie algebras of both classical and exceptional types. We also give a counter-example in type D7. |
| Starting Page | 69 |
| Ending Page | 72 |
| Page Count | 4 |
| File Format | PDF HTM / HTML |
| Volume Number | 1945 |
| Alternate Webpage(s) | https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/223850/1/1945-07.pdf |
| Alternate Webpage(s) | http://hal.inria.fr/docs/00/86/63/56/PDF/symmetric_invariants.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
