Capelli elements in the classical universal enveloping algebras
| dc.creator | Nazarov, Maxim | |
| dc.date | 1998-11-22 | |
| dc.date.accessioned | 2026-07-07T05:26:57Z | |
| dc.date.available | 2026-07-07T05:26:57Z | |
| dc.description | For any complex classical group $G=O_N,Sp_N$ consider the ring $Z(g)$ of $G$-invariants in the corresponding enveloping algebra $U(g)$. Let $u$ be a complex parameter. For each $n=0,1,2,...$ and every partition $ν$ of $n$ into at most $N$ parts we define a certain rational function $Z_ν(u)$ which takes values in $Z(g)$. Our definition is motivated by the works of Cherednik and Sklyanin on the reflection equation, and also by the classical Capelli identity. The degrees in $U(g)$ of the values of $Z_ν(u)$ do not exceed $n$. We describe the images of these values in the $n$-th symmetric power of $g$. Our description involves the plethysm coefficients as studied by Littlewood, see Theorem 3.4 and Corollary 3.6. | |
| dc.description | 24 pages, AmS-TeX | |
| dc.identifier | https://arxiv.org/abs/math/9811129 | |
| dc.identifier | http://arxiv.org/abs/math/9811129 | |
| dc.identifier | Adv. Studies Pure Math. 28 (2000), 261-285 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77747 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.title | Capelli elements in the classical universal enveloping algebras | |
| dc.type | text |