On the irreducible representations of the alternating group which remain irreducible in characteristic $p$

ON THE IRREDUCIBLE REPRESENTATIONS OF THE ALTERNATING GROUP WHICH REMAIN IRREDUCIBLE IN CHARACTERISTIC p

We consider the problem of which ordinary irreducible representations of the alternating group An remain irreducible modulo a prime p. We solve this problem for p = 2, and present a conjecture for odd p, which we prove in one direction.

Representations of the Alternating Group Which Are Irreducible over Subgroups

CHARACTERS OF THE IRREDUCIBLE REPRESENTATIONS WITH FUNDAMENTAL HIGHEST WEIGHT FOR THE SYMPLECTIC GROUP IN CHARACTERISTIC p

Abstract. Let K be an algebraically closed field of characteristic p > 0 and let Sp(2m) be the symplectic group of rank m over K. The main theorem of this article gives the character of the rational simple Sp(2m)-modules with fundamental highest weight as an explicit alternating sum of characters of Weyl modules. One obtains several formulae for the dimensions of these simple modules, what allo...

Irreducible Representations of the Symmetric Group

We construct the Specht modules and prove that they completely characterize the irreducible representations of the symmetric group. We will prove certain properties of these representations using combinatorial tools (such as calculating the dimension using Hook’s length formula). Only an introductory knowledge of group theory and linear algebra will be assumed and representation theory concepts...

Irreducible canonical representations in positive characteristic

For X a curve over a field of positive characteristic, we investigate when the canonical representation of Aut(X) on H0(X , X) is irreducible. Any curve with an irreducible canonical representation must either be superspecial or ordinary. Having a small automorphism group is an obstruction to having irreducible canonical representation; with this motivation, the bulk of the paper is spent bound...