Irreducible representations of the alternating group in odd characteristic

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

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...

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...

Dimensions of the Irreducible Representations of the Symmetric and Alternating Group

We establish the existence of an irreducible representation of An whose dimension does not occur as the dimension of an irreducible representation of Sn, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in the proof is a result on large prime factors in short intervals.