A Bijection for the Alperin Weight Conjecture in S-n

作者：Cossey James P^*

来源：Algebras and Representation Theory, 2011, 14(2): 391-402.

DOI：10.1007/s10468-009-9194-x

• Symmetric groups
• Representations
• Weights

The Alperin weight conjecture states that if G is a finite group and p is a prime, then the number of irreducible Brauer characters of a group G should be equal to the number of conjugacy classes of p-weights of G. This conjecture is known to be true for the symmetric group S (n) , however there is no explicit bijection given between the two sets. In this paper we develop an explicit bijection between the p-weights of S (n) and a certain set of partitions that is known to have the same cardinality as the irreducible Brauer characters of S (n) . We also develop some properties of this bijection, especially in relation to a certain class of partitions whose corresponding Specht modules over fields of characteristic p are known to be irreducible.

• 出版日期2011-4