Deligne categories as limits in rank and characteristic
Abstract
We give new interpretations of the Deligne categories
Rep
–
–
–
–
(G
L
t
)
and
Rep
–
–
–
–
(
S
t
)
(and their abelian envelopes) over
C
in terms of modular representations of general linear and symmetric groups of large rank in large characteristic. In particular we make sense of the sentence "
Rep
–
–
–
–
(
S
n
)
is the limit of
Rep(
S
p+n
)
over
F
¯
p
as
p
goes to infinity". We then give examples of how to pass results between these different settings.