Elementary divisors of Specht modules
| dc.creator | Künzer, Matthias | |
| dc.creator | Mathas, Andrew | |
| dc.date | 2003-09-26 | |
| dc.date | 2004-07-01 | |
| dc.date.accessioned | 2026-07-07T05:01:27Z | |
| dc.date.available | 2026-07-07T05:01:27Z | |
| dc.description | Let H_q(S_n) be the Iwahori-Hecke algebra of the symmetric group. This algebra is semisimple over the rational function field Q(q), where q is an indeterminate, and its irreducible representations over this field are q-analogues S_q(lambda) of the Specht modules of the symmetric group. The q-Specht modules have an "integral form" which is defined over the Laurent polynomial ring Z_[q,q^{-1}] and they come equipped with a natural bilinear form with values in this ring. Now Z[q,q^{-1}] is not a principal ideal domain. Nonetheless, we try to compute the elementary divisors of the Gram matrix of the bilinear form on S_q(lambda). When they are defined, we give a precise relationship between the elementary divisors of the Specht modules S_q(lambda) and S_q(lambda'), where lambda' is the conjugate partition. We also compute the elementary divisors when lambda is a hook partition and give examples to show that in general elementary divisors do not exist. | |
| dc.description | Sign mistake in 6.5 ff. corrected. European J. Combinatorics (to appear) | |
| dc.identifier | https://arxiv.org/abs/math/0309426 | |
| dc.identifier | http://arxiv.org/abs/math/0309426 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68680 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | 20C08, 20G05, 33D80 | |
| dc.title | Elementary divisors of Specht modules | |
| dc.type | text |