On the decomposition map for symmetric groups
نویسندگان
چکیده
منابع مشابه
On the decomposition map for symmetric groups
Let R be the Z-module generated by the irreducible characters of the symmetric group Sd . We determine bases for the kernel of the decomposition map. It is known that R ⊗Z F is isomorphic to the radical quotient of the Solomon descent algebra when F is a field of characteristic zero. We show that when F has prime characteristic and I d br is the kernel of the decomposition map for prime p then ...
متن کاملDecomposition numbers for symmetric groups
Where to find decomposition matrices? Try www.math.rwth-aachen.de/∼MOC In hard copy, [6] has several (at the end) for small primes. For p = 2, a paper by Juergen Mueller(Aachen) [7], for an electronic version try his homepage. General background can be found in [6]. Column removal: Due to G.D. James, sometime after '76. Just now I cannot find the precise reference. However, a generalization of ...
متن کاملThe 2-modular Decomposition Matrices of the Symmetric Groups
In this paper the 2-modular decomposition matrices of the symmetric groups S15, S16, and S17 are determined by application of methods from computational representation theory, in particular condensation techniques, and by using the computer algebra systems GAP, MOC, and the MeatAxe.
متن کاملCharacter values and decomposition matrices of symmetric groups
The relationships between the values taken by ordinary characters of symmetric groups are exploited to prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd characteristic have distinct rows. In characteristic 2 the rows of a decomposition matrix labelled by the different partitions λ and μ are equal if and only ...
متن کاملPower Map Permutations and Symmetric Differences in Finite Groups
Let G be a finite group. For all a ∈ Z, such that (a, |G|) = 1, the function ρa : G → G sending g to g defines a permutation of the elements of G. Motivated by a recent generalization of Zolotarev’s proof of classic quadratic reciprocity, due to Duke and Hopkins, we study the signature of the permutation ρa. By introducing the group of conjugacy equivariant maps and the symmetric difference met...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2008
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-008-0134-3