Properties of some character tables related to the symmetric groups
| dc.creator | Bessenrodt, Christine | |
| dc.creator | Olsson, Jorn B. | |
| dc.creator | Stanley, Richard P. | |
| dc.date | 2004-03-05 | |
| dc.date.accessioned | 2026-07-07T05:06:08Z | |
| dc.date.available | 2026-07-07T05:06:08Z | |
| dc.description | We determine invariants like the Smith normal form and the determinant for certain integral matrices which arise from the character tables of the symmetric groups S_n and their double covers. In particular, we give a simple computation, based on the theory of Hall-Littlewood symmetric functions, of the determinant of the regular character table of S_n with respect to an integer r>1. This result had earlier been proved by Olsson in a longer and more indirect manner. As a consequence, we obtain a new proof of the Mathas' Conjecture on the determinant of the Cartan matrix of the Iwahori-Hecke algebra. When r is prime we determine the Smith normal form of the regular character table. Taking r large yields the Smith normal form of the full character table of S_n. Analogous results are then given for spin characters. | |
| dc.identifier | https://arxiv.org/abs/math/0403110 | |
| dc.identifier | http://arxiv.org/abs/math/0403110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70371 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 05E10; 20C30 | |
| dc.title | Properties of some character tables related to the symmetric groups | |
| dc.type | text |