Representations of twisted Yangians associated with skew Young diagrams
| dc.creator | Nazarov, Maxim | |
| dc.date | 2002-07-13 | |
| dc.date | 2004-04-05 | |
| dc.date.accessioned | 2026-07-07T04:49:40Z | |
| dc.date.available | 2026-07-07T04:49:40Z | |
| dc.description | Let $G_M$ be one of the complex Lie groups $O_M$ and $Sp_M$. The irreducible finite-dimensional representations of the group $G_M$ are labeled by partitions $μ$ satisfying certain extra conditions. Let $U$ be the representation of $G_M$ corresponding to $μ$. Regard the direct product $G_N\times G_M$ as a subgroup of $G_{N+M}$. Let $V$ be the irreducible representation of $G_{N+M}$ corresponding to a partition $λ$. Consider the vector space $W=Hom_{G_M}(U,V)$. It comes with a natural action of the group $G_N$. Let $n$ be sum of parts of $λ$ less the sum of parts of $μ$. For any choice of a standard Young tableau of skew shape $λ/μ$, we realize $W$ as a subspace in the tensor product of $n$ copies of the defining $N$-dimensional representation of $G_N$. This subspace is determined as the image of a certain linear operator $F(M)$ in the tensor product, given by an explicit formula. When M=0 and $W=V$ is an irreducible representation of $G_N$, we recover the classical realization of $V$ as a subspace in the space of all traceless tensors. Then the operator F(0) can be regarded as the analogue for $G_N$ of the Young symmetrizer, corresponding to the chosen standard tableau of shape $λ$. Even in the special case M=0, our formula for the operator $F(M)$ is new. Our results are applications of representation theory of the twisted Yangian, corresponding to $G_N$. In particular, $F(M)$ is an intertwining operator between two representations of the twisted Yangian in the $n$-fold tensor product. | |
| dc.description | 60 pages; final version, Section 0 added | |
| dc.identifier | https://arxiv.org/abs/math/0207115 | |
| dc.identifier | http://arxiv.org/abs/math/0207115 | |
| dc.identifier | Selecta Math. 10 (2004), 71-129 | |
| dc.identifier | doi:10.1007/s00029-004-0350-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64508 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B35; 17B37; 20C30; 22E46; 81R50 | |
| dc.title | Representations of twisted Yangians associated with skew Young diagrams | |
| dc.type | text |