We analyze the structure of the algebra K〈x〉n of symmetric polynomials in non-commuting variables in so far as it relates to K[x]n , its commutative counterpart. Using the “place-action” of the symmetric group, we are able to realize the latter as the invariant polynomials inside the former. We discover a tensor product decomposition of K〈x〉n analogous to the classical theorems of Chevalley, Sh...

We study a particular class of transition kernels that stems from differentiating Markov kernels in the weak sense. Sufficient conditions are established for this type of kernels to admit a Jordan-type decomposition. The decomposition is explicitly constructed.

We prove a Chevalley restriction theorem and its double analogue for the cyclic quiver. The aim of this paper is to prove a Chevalley restriction theorem and its double analogue for the cyclic quiver. When the quiver is of type Â0, we recover the results for gln. The proof of our Chevalley restriction theorem is similar to the proof for gln; however, the proof of the double analogue uses a theo...

Clifford algebras are naturally associated with quadratic forms. These algebras are Z2 -graded by construction. However, only a Zn -gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V ) ↔ ∧ V and an ordering, guarantees a multivector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomor...

W. Plesken found a simple but interesting construction of a Lie algebra from a finite group. Cohen and Taylor posed themselves the question of what the Plesken Lie algebra, which is the Lie subalgebra of the group algebra k[G] generated by the elements g − g−1, could be. The result is very fascinating: It turns out that the Lie algebra decomposition of the Plesken Lie algebra into simple Lie al...

A new geometric proof is given for the standard description of subgroups in the Chevalley group G = G(F4, R) of type F4 over a commutative ring R that are normalized by the elementary subgroup E(F4, R). There are two major approaches to the proof of such results. Localization proofs (Quillen, Suslin, Bak) are based on a reduction in the dimension. The first proofs of this type for exceptional g...

There is substantial evidence that on average, urban children have better health outcomes than rural children. This paper investigates the underlying factors that account for the regional disparities in child malnutrition in three Arab countries, namely; Egypt, Jordan, and Yemen. We use data on a nationally representative sample from the most recent rounds of the Demographic and Health Survey. ...

Having deened a notion of homology for paired graphs, M etayer ((Ma]) proves a ho-mological correctness criterion for proof nets, and states that for any proof net G there exists a Jordan-HH older decomposition of H 0 (G). This decomposition is determined by a certain enumeration of the pairs in G. We correct his proof of this fact and show that there exists a 1-1 correspondence between these J...

The Bonnafé–Rouquier equivalence can be seen as a modular analogue of Lusztig’s Jordan decomposition for groups Lie type. In this paper, we show that lifted to include automorphisms the finite group Moreover, prove existence local version which satisfies similar properties.