Abstract
In this paper we prove two conjectures on partitions with certain conditions. A motivation for this is given by a problem in the modular representation theory of the covering groups Sn of the finite symmetric groups Sn in characteristic 5. One of the conjectures (Conjecture B below) has been open since 1974, when it was stated by the first author in his memoir [A3]. Recently the second and third author (jointly with A. O. Morris) arrived at essentially the same conjecture from a completely different direction. Their paper [BMO] was concerned with decomposition matrices of Sn in characteristic 3. A basic difficulty for obtaining similar results in characteristic 5 (or larger) was the lack of a class of partitions which would be "natural" character labels for the modular characters of these groups. In this connection two conjectures were stated (Conjectures A and B below), whose solutions would be helpful in the characteristic 5 case. One of them, Conjecture B, is equivalent to the old Conjecture B mentioned above. Conjecture A is concerned with a possible inductive definition of the set of partitions which should serve as the required labels.
Original language | English (US) |
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Pages (from-to) | 597-615 |
Number of pages | 19 |
Journal | Transactions of the American Mathematical Society |
Volume | 344 |
Issue number | 2 |
DOIs | |
State | Published - Aug 1994 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics