‎Let $V$ be an $n$-dimensional complex inner product space‎. ‎Suppose‎ ‎$H$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎Hrightarrow mathbb{C} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎Denote by $V_{chi}(H)$ the symmetry class‎ ‎of tensors associated with $H$ and $chi$‎. ‎Let $K(T)in‎ (V_{chi}(H))$ be the operator induced by $Tin‎ ‎text{End}(V)$‎. ‎Th...

‎Let $G$ be a finite group‎. ‎An element $gin G$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $chi$ of $G$‎, ‎$chi(g)neq 0$‎. ‎The bi-Cayley graph ${rm BCay}(G,T)$ of $G$ with respect to a subset $Tsubseteq G$‎, ‎is an undirected graph with‎ ‎vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin G‎, ‎ tin T}$‎. ‎Let ${rm nv}(G)$ be the set‎ ‎of all non-vanishi...

Recently, there has been considerable progress in classifying the irreducible representations of Iwahori–Hecke algebras at roots of unity. Here, we present an application of these results to l-modular Harish–Chandra series for a finite group of Lie type G(q). Under some mild condition on l, we show that the l-modular principal series representations of G(q) are naturally parametrized by a subse...

Abstract We prove that the maximal number of conics in a smooth sextic $K3$ -surface $X\subset \mathbb {P}^4$ is 285, whereas real 261. In both extremal configurations, all are irreducible.

Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.

A non-empty subset of a topological space is irreducible if whenever it is covered by the union of two closed sets, then already it is covered by one of them. Irreducible sets occur in proliferation: (1) every singleton set is irreducible, (2) directed subsets (which of fundamental status in domain theory) of a poset are exactly its Alexandroff irreducible sets, (3) directed subsets (with respe...

Let k be a perfect field, and X an irreducible smooth projective curve over k. We give criterion for vector bundle to admit logarithmic connection singular finite subset of with given residues, where residues are assumed rigid.

Let Mg be the moduli space of smooth, genus g curves over an algebraically closed field K of zero characteristic. Denote by Mg(G) the subset of Mg of curves δ such that G (as a finite non-trivial group) is isomorphic to a subgroup of Aut(δ), the full automorphism group of δ, and let M̃g(G) be the subset of curves δ such that G ∼= Aut(δ). Now, for an integer d ≥ 4, let MPl g be the subset of Mg r...