A basic set for the alternating group

Restriction of characters to subgroups of wreath products and basic sets for the symmetric group

“…In [1], the authors describe, for any integer n and odd prime p, a p-basic set B for the symmetric group S n . The object of the present paper is, in this case, to describe completely the matrix N B .…”

“…. , λ p ) with λ r = ∅} be the p-basic set for b constructed in [1]. The results of [1] show that there is an explicit bijection χ λ −→ χλ from Irr(b) to itself, which restricts to the identity on B b , as well as explicitly determined signs {ε(λ) ,…”

Basic Sets for the Double Covering Groups of the Symmetric and Alternating Groups in Odd Characteristic

“…While it is unclear how to exhibit a p-basic set of G in general, Hiss conjectured that all finite groups do have p-basic sets. This conjecture is true in the following cases: for p-soluble groups [11, X.2.1], for certain finite reductive groups under various assumptions ( [17], [12], [15], [13], [14], [22], [10], [6]), and for symmetric and alternating groups ( [21], [9], [8], [2]).…”

A 2-basic set of the alternating group

“…For any B ⊆ Irr(S n ), we call restriction of B to A n the subset B An of Irr(A n ) consisting of all the irreducible constituents of the restrictions to A n of the characters in B. To prove the existence of a p-basic set of A n for odd prime p, the approach in [3] consists in constructing a p-basic set B of S n satisfying two additional properties which ensure that B An is a p-basic set of A n (cf. [3, 1.1]).…”

“…The aim of this paper is to adapt the methods of [3] (some of which heavily relie on p being odd) to the case p = 2, in order to construct a 2-basic set of S n satisfying Proposition 1.1.…”