On the decomposition map for symmetric groups
نویسنده
چکیده
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 R/I br ⊗ZF is isomorphic to the radical quotient of the p-modular Solomon descent algebra.
منابع مشابه
Properties of eigenvalue function
For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.
متن کاملDECOMPOSITION METHOD FOR SOLVING FULLY FUZZY LINEAR SYSTEMS
In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.
متن کاملOn a functional equation for symmetric linear operators on $C^{*}$ algebras
Let $A$ be a $C^{*}$ algebra, $T: Arightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),;;T(x^{*})=T(x)^{*} $. We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=lambda x$ for some $lambda in mathbb{R}$: i) $A$ is a simple $C^{*}$-algebra. ii) $A$ is unital with trivial center and has a faithful trace such ...
متن کاملSymmetric Chain Decomposition for Cyclic Quotients of Boolean Algebras and Relation to Cyclic Crystals
The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order, giving an explicit construction for any order, prime or composite. The combinatorial map specifying how to proceed downward in a symmetric chain is shown to be a natural cyclic analogue of the sl2 lowering ...
متن کاملTheoretical study of the influence of solvent polarity on the structure and spectral properties in the interaction of C20 and Si2H2
In this investigation, the interaction of C20 and Si2H2 molecules was explored in the M06-2X/6-311++G(d,p)level of theory in gas solution phases. The obtained interaction energy values with standard method werecorrected by basis set superposition error (BSSE) during the geometry optimization for all molecules atthe same level of theory. Also, the bonding interaction between th...
متن کامل