This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin’s weight conjecture on the p-blocks of a finite group would imply some arithmetical conditions on the degrees of the irreducible (complex) characters of that group. The purpose of this note is to prove directly that one of these arithmetical conditions is true...

This paper presents a realtime performance animation system that reproduces full-body character animation based on sparse 3D motion sensors on the performer. Producing faithful character animation from this setting is a mathematically ill-posed problem because input data from the sensors is not sufficient to determine the full degrees of freedom of a character. Given the input data from 3D moti...

Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is a Mathieu group such that cd(G) = cd(H), then there exists an abelian subgroup A of G such that G/A is isomorphic to H. In view of Huppert’s conjecture (2000), we also provide some examples to show that...

A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S 6 G 6 Aut(S) for a finite simple group S. More generally, we show that ifG is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups....

We define a map of simplicial presheaves, the Chern character, that assigns to every sequence composable non connection preserving isomorphisms vector bundles with holomorphic connections an appropriate forms. apply this character Cech nerve good cover complex manifold and assemble data by passing totalization obtain sets. In degree 0, gives formula for bundle in terms clutching functions. 1, m...

Let G be a finite group. The character degree graph [Formula: see text] of G is the graph whose vertices are the prime divisors of character degrees of G and two vertices p and q are joined by an edge if pq divides the character degree of G. Let [Formula: see text] be the projective special linear group of degree n over a finite field of order q. Khosravi et. al. have shown that the simple grou...

This paper presents a real-time performance animation system that reproduces fullbody character animation based on sparse 3Dmotion sensors on a performer. Producing 1 In Computer Animation and Virtual Worlds, 24(6), 565-576, 2013 This version is the author's manuscript. faithful character animation from this setting is a mathematically ill-posed problem because input data from the sensors are n...

Let G be a finite group and Irr ( ) the set of all complex irreducible characters . The character-graph Δ associated to , is graph whose vertex primes which divide degrees some in two distinct p q are adjacent if product pq divides χ 1 for ∈ Tong-Viet posed conjecture that k -regular integer ⩾ 2 then either complete or cocktail party graph. In this paper, we show his true regular character-grap...