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Character-degree valuation does not increase on taking the p-core
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Representation theory of the symmetric group
Partition of an integer
Beta set of a partition
Abacus of a partition
Core tower of a partition
P-adic valuation of a symmetric-group character degree from the core tower
2026-09-28
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For every partition
λ
,
v
p
(
χ
λ
(
1
))
≥
v
p
(
χ
C
p
(
λ
)
(
1
))
.
(1)
The core-tower
formula
reduces this to
subadditivity
of the base-
p
digit sum
across the
sizes
of the
quotient
partitions.
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(11)
P-adic valuation of a symmetric-group character degree from the core tower
Core tower of a partition
Abacus of a partition
Beta set of a partition
Partition of an integer
Representation theory of the symmetric group
Representation theory
Algebra
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 160
/
4
/
c
/
Solution
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