Elementary divisors of Gram matrices of certain Specht modules
نویسنده
چکیده
The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely, the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover, considering a general partition λ of n at a prime p > n − λ 1 , the only possible non trivial composition factor of S λ Fp is induced by the morphism of Carter and Payne, as shown by means of Kleshchev's modular branching rule. This enables the Jantzen filtration to be calculated in this case as well. 3 At a large prime 22 4 Transposition 24 0 AMS subject classification: 20C30.
منابع مشابه
divisors of Gram matrices of certain Specht modules
The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely, the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover, considering a general partition λ of n at a prime p > n − λ 1 , the only possible non trivial composition factor of S λ Fp is...
متن کاملElementary divisors of Specht modules
The irreducible representations of the symmetric groups and their Iwahori-Hecke algebras have been classified and constructed by James [6] and Dipper and James [2], yet simple properties of these modules, such as their dimensions, are still not known. Every irreducible representation of these algebras is constructed by quotienting out the radical of a bilinear form on a particular type of modul...
متن کامل2 9 Ju l 2 00 3 Elementary divisors of Gram matrices of certain
The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely, the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover, considering a general partition λ of n at a prime p > n − λ 1 , the only possible non trivial composition factor of S λ Fp is...
متن کاملMatthias Künzer And
The irreducible representations of the symmetric groups and their Iwahori-Hecke algebras have been classified and constructed by James [6] and Dipper and James [2], yet simple properties of these modules, such as their dimensions, are still not known. Every irreducible representation of these algebras is constructed by quotienting out the radical of a bilinear form on a particular type of modul...
متن کاملOn nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
متن کامل