We say that a coherent configuration is of Chevalley type if its basis relations correspond to orbitals of a geometric action (G,Ω), where G is a finite Chevalley group. If the action is transitive, the resulting configuration is an association scheme. In this paper, we seek to provide an effective universal strategy for orbital recognition in coherent configurations of Chevalley type. This mus...

In 1935, C. Chevalley proved a conjecture by E. Artin: if F ðX1; . . . ; XmÞ is a homogeneous polynomial of total degree d < m over a 7nite 7eld Fq having q 1⁄4 p elements, then F has a non-trivial zero. Chevalley showed the result to hold even when the homogeneity hypothesis is replaced by the weaker requirement that F ðX1; . . . ; XmÞ has no constant term. Almost immediately, E. Warning showe...

in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

We develop a notion of degree for functions between two abelian groups that allows us to generalize the Chevalley Warning Theorems from fields noncommutative rings or prime power order.

In this paper we study the MOR cryptosystem with finite Chevalley groups. There are four infinite families of finite classical Chevalley groups. These are: special linear groups SL(d, q), orthogonal groups O(d, q) and symplectic groups Sp(d, q). The family O(d, q) splits to two different families of Chevalley groups depending on the parity of d. The MOR cryptosystem over SL(d, q) was studied by...

Peterson varieties are a special class of Hessenberg varieties that have been extensively studied e.g. by Peterson, Kostant, and Rietsch, in connection with the quantum cohomology of the flag variety. In this manuscript, we develop a generalized Schubert calculus, and in particular a positive Chevalley-Monk formula, for the ordinary and Borel-equivariant cohomology of the Peterson variety Y in ...