Quantum alpha-determinants and q-deformed hypergeometric polynomials
| dc.creator | Kimoto, Kazufumi | |
| dc.date | 2009-02-26 | |
| dc.date.accessioned | 2026-07-07T12:47:09Z | |
| dc.date.available | 2026-07-07T12:47:09Z | |
| dc.description | The quantum $α$-determinant is defined as a parametric deformation of the quantum determinant. We investigate the cyclic $\mathcal{U}_q(\mathfrak{sl}_2)$-submodules of the quantum matrix algebra $\mathcal{A}_q(\mathrm{Mat}_2)$ generated by the powers of the quantum $α$-determinant. For such a cyclic module, there exists a collection of polynomials which describe the irreducible decomposition of it in the following manner: (i) each polynomial corresponds to a certain irreducible $\mathcal{U}_q(\mathfrak{sl}_2)$-module, (ii) the cyclic module contains an irreducible submodule if the parameter is a root of the corresponding polynomial. These polynomials are given as a $q$-deformation of the hypergeometric polynomials. This is a quantum analogue of the result obtained in our previous work [K. Kimoto, S. Matsumoto and M. Wakayama, Alpha-determinant cyclic modules and Jacobi polynomials, to appear in Trans. Amer. Math. Soc.]. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0902.4608 | |
| dc.identifier | http://arxiv.org/abs/0902.4608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221619 | |
| dc.subject | Representation Theory | |
| dc.subject | 20G42; 33C20 | |
| dc.title | Quantum alpha-determinants and q-deformed hypergeometric polynomials | |
| dc.type | text |