Abstract
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.
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References
Alperin, J.L., Fong, P.: Weights for symmetric and general linear groups. J. Algebra 131, 2–22 (1990)
Fayers, M.: Irreducible Specht modules for Hecke algebras of type A. Adv. Math. 193, 438–452 (2005)
Fong, P.: The Isaacs-Navarro conjecture for symmetric groups. J. Algebra 260, 154–161 (2003)
Isaacs, I.M., Navarro, G.: Weights and vertices for characters of π-separable groups. J. Algebra 177, 339–366 (1995)
James, G.D., Kerber, A.: The Representation Theory of the Symmetric Group. Addison-Wesley, Reading (1981)
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Cossey, J.P. A Bijection for the Alperin Weight Conjecture in S n . Algebr Represent Theor 14, 391–402 (2011). https://doi.org/10.1007/s10468-009-9194-x
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DOI: https://doi.org/10.1007/s10468-009-9194-x