Representation theory of the $α$-determinant and zonal spherical functions
| dc.creator | Kimoto, Kazufumi | |
| dc.date | 2007-12-14 | |
| dc.date.accessioned | 2026-07-07T08:49:16Z | |
| dc.date.available | 2026-07-07T08:49:16Z | |
| dc.description | We prove that the multiplicity of each irreducible component in the $\mathcal{U}(\mathfrak{gl}_n)$-cyclic module generated by the $l$-th power $\det^{(α)}(X)^l$ of the $α$-determinant is given by the rank of a matrix whose entries are given by a variation of the spherical Fourier transformation for $(\mathfrak{S}_{nl},\mathfrak{S}_l^n)$. Further, we calculate the matrix explicitly when $n=2$. This gives not only another proof of the result by Kimoto-Matsumoto-Wakayama (2007) but also a new aspect of the representation theory of the $α$-determinants. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0712.2293 | |
| dc.identifier | http://arxiv.org/abs/0712.2293 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144237 | |
| dc.subject | Representation Theory | |
| dc.subject | 22E47; 43A90 | |
| dc.title | Representation theory of the $α$-determinant and zonal spherical functions | |
| dc.type | text |