Definition 9.1.3. An additive character of F is a character of the additive group F, i.e. a map χ : (F,+) → T, with χ(a+ b) = χ(a)χ(b). Now, let Fq denote the field of order q = p . We can define it by Fq := Fp[x]/(f), where f is any irreducible polynomial of degree k. We know that Fq is a cyclic group of order q − 1, and is generated by some g ∈ Fq (in other word Fq = 〈g〉). That is, g = 1 and ...

‎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 $bcay(g,t)$ 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 $nv(g)$ be the set‎ ‎of all non-vanishing element...

We compute both natural and smooth models for the SL2(C) character varieties of the two component double twist links, an infinite family of two-bridge links indexed as J(k, l). For each J(k, l), the component(s) of the character variety containing characters of irreducible representations are birational to a surface of the form C × C where C is a curve. The same is true of the canonical compone...

Kronecker products of complex characters of the symmetric group Sn have been studied in many papers. Information on special products and on the coefficients of special constituents have been obtained but there is no efficient combinatorial algorithm in sight for computing these products. In [1], products of Sn-characters with few homogeneous components and homogeneous products of characters of ...

We show that the irreducible variety of 4 × 4 × 4 complex valued tensors of border rank at most 4 is the zero set of polynomial equations of degree 5 (the Strassen commutative conditions), of degree 6 (the Landsberg-Manivel polynomials), and of degree 9 (the symmetrization conditions).

Let G be a finite group, and let $$\textrm{cd}(G)$$ denote the set of degrees irreducible complex characters G. Define then character degree graph $$\Delta (G)$$ as (simple undirected) whose vertices are prime divisors numbers in , two distinct p, q adjacent if only pq divides some number . This paper continues work, started [8], toward classification non-solvable groups possesses cut-vertex, i...

Denote by S the projective special linear group PSL2(q) over the field of q elements. We determine, for all values of q > 3, the degrees of the irreducible complex characters of every group H such that S 6 H 6 Aut(S). We also determine the character degrees of certain extensions of the special linear group SL2(q). Explicit knowledge of the character tables of SL2(q), GL2(q), PSL2(q), and PGL2(q...