Representations of finite special linear groups in non-defining characteristic

Representations of Finite Special Linear Groups in Non-defining Characteristic Alexander S. Kleshchev and Pham Huu Tiep

1.1. Background. Let q = pf be a power of a prime number p, and SLn(q) = SLn(Fq) be the special linear group over the field Fq with q elements. Let F be an algebraically closed field of characteristic l ≥ 0. We are interested in parametrizing irreducible representations of SLn(q) over F. If l = p, this is well known: a parametrization is given by the so-called q-restricted dominant weights, see...

Small degree representations of finite Chevalley groups in defining characteristic

We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l our bound is proportional to l3 and for rank 11 m...

Linear Representations of Finite Groups

ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

Some Representations of Special Linear Groups

Mat r x ( F q ) o f a l l r b y r m a t r i c e s o v e r F q , b y C t h e g r o u p G L t i ( F q ) o f t h e u n i t s of M, and by S the special linear subgroup SL , (F q ) o f C . F o r a n a r b i t r a r y field F containing F q , l e t U s t a n d f o r t h e ( c o m m u t a t i v e ) p o l y n o m i a l a l g e b r a F[xl, , x r ] , a n d c o n s i d e r U g r a d e d a s u s u a l : U...