Let GF be a finite group of Lie type, where G is reductive defined over F¯q and F Frobenius root. Lusztig’s Jordan decomposition parametrises the irreducible characters in rational series E(GF,(s)G∗F∗) s∈G∗F∗ by E(CG∗(s)F∗,1). We conjecture that Shintani twisting preserves space class functions generated union E(GF,(s′)G∗F∗) (s′)G∗F∗ runs semi-simple classes G∗F∗ geometrically conjugate to s; f...

N. L. Gordeev proved that a generalized group identity holds in Chevalley groups with multiply laced root systems. It was also shown that a stronger identity is valid for the Chevalley groups of types Bl and Cl. In the present paper, it is proved that this strong identity is fulfilled in Chevalley groups of type F4 and fails to be true in Chevalley groups of type G2. The main result of the pape...

We derive a closed form for the Jordan decomposition of companion matrices including properties of generalized eigenvectors. As a consequence, we provide a formula for the inverse of confluent Vandermonde matrices and results on sensitivity of multiple roots of polynomials.

The paper is devoted to a detailed study of some remarkable semisimple elements of (extended) Chevalley groups that are diagonalizable over the ground field — the weight elements. These are the conjugates of certain semisimple elements hω(ε) of extended Chevalley groupsG = G(Φ, K), where ω is a weight of the dual root system Φ∨ and ε ∈ K∗. In the adjoint case the hω(ε)’s were defined by Chevall...

This work is concerned with multi-party stabilizer states in the sense of quantum information theory. We investigate the homological invariants for states of which each party holds a large equal number N of quantum bits. We show that in many cases there is a generic expected value of the invariants : for large N it is approximated with arbitrarily high probability if a stabilizer state is chose...