Regular Elements and Monodromy of Discriminants of Finite Reflection Groups

Equivariant Euler Characteristics of Discriminants of Reflection Groups

Let G be a finite, complex reflection group acting on a complex vector space V , and δ its disciminant polynomial. The fibres of δ admit commuting actions of G and a cyclic group. The virtual G×Cm character given by the Euler characteristic of a fibre is a refinement of the zeta function of the geometric monodromy, calculated in [8]. We show that this virtual character is unchanged by replacing...

A Few Problems on Monodromy and Discriminants

The article contains several problems concerning local monodromy groups of singularities, Lyashko–Looijenga maps, integral geometry, and topology of spaces of real algebraic manifolds.

Regular Elements of Finite Reflection Groups

On the Finite Groupoid G(n)

In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) to be commuting regular.

On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups

Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|...