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) |
|---|---|
| Pages (from-to) | 597-615 |
| Number of pages | 19 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 344 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 1 1994 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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Partition identities and labels for some modular characters. / Andrews, George E.; Bessenrodt, C.; Olsson, J. B.
In: Transactions of the American Mathematical Society, Vol. 344, No. 2, 01.01.1994, p. 597-615.Research output: Contribution to journal › Article
TY - JOUR
T1 - Partition identities and labels for some modular characters
AU - Andrews, George E.
AU - Bessenrodt, C.
AU - Olsson, J. B.
PY - 1994/1/1
Y1 - 1994/1/1
N2 - 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.
AB - 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.
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U2 - 10.1090/S0002-9947-1994-1220904-1
DO - 10.1090/S0002-9947-1994-1220904-1
M3 - Article
VL - 344
SP - 597
EP - 615
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 2
ER -