Schur-Weyl Reciprocity for the Hecke Algebra of $(\Bbb Z/r\Bbb Z)\wr \frak S_n$
| dc.creator | Ariki, Susumu | |
| dc.creator | Terasoma, Tomohide | |
| dc.creator | Yamada, Hirofumi | |
| dc.date | 1993-10-14 | |
| dc.date.accessioned | 2026-07-07T04:19:45Z | |
| dc.date.available | 2026-07-07T04:19:45Z | |
| dc.description | The purpose of this paper is to give a reciprocity between $U_q(h)$ and $\Cal H_{n,r}$, the Hecke algebra of $(\Bbb Z / r\Bbb Z)\wr \frak S_n$ introduced by Ariki and Koike. Let $K=\Bbb Q(q,u_1,\dots ,u_r)$ be the field of rational funcitons in variables $q,u_1,\dots ,u_r$. We adopt $K$ as the base field for both the quantized universal enveloping algebra $U_q(gl_r)$ and the Hecke algebra $\Cal H_n$. We denote by $U_q(h)$ the $K$-subalgebra of $U_q(gl_r)$ generated by $q^{E_{ii}}\;$'s $(1\le i \le r)$. In this paper, we show that the commutant of $U_q(h)$ in $End((K^r)^{\otimes n})$ is isomorphic to a quotient of $\Cal H_{n,r}$. We also determine the irreducible decomposition of $(K^r)^{\otimes n}$ under the action of $\Cal H_{n,r}$. As a consequence, we obtain the reciprocity for $U_q(h)$ and $\Cal H_{n,r}$. | |
| dc.description | 15 | |
| dc.identifier | https://arxiv.org/abs/hep-th/9310078 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9310078 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/53687 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Schur-Weyl Reciprocity for the Hecke Algebra of $(\Bbb Z/r\Bbb Z)\wr \frak S_n$ | |
| dc.type | text |