TY - JOUR
T1 - Deligne categories and the limit of categories rep(gl(m|n))
AU - Entova-Aizenbud, Inna
AU - Hinich, Vladimir
AU - Serganova, Vera
N1 - Publisher Copyright: © 2020 Oxford University Press. All rights reserved.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - For each integer t a tensor category V t is constructed, such that exact tensor functors V t - C classify dualizable t-dimensional objects in C not annihilated by any Schur functor. This means that V t is the “abelian envelope” of the Deligne category D t = Rep(GLt). Any tensor functor Rep(GLt) -C is proved to factor either through V t or through one of the classical categories Rep(GL(m|n)) with m - n = t. The universal property of V t implies that it is equivalent to the categories RepDt1 Dt2 (GL(X),), (t = t1 + t2, t1 not an integer) suggested by Deligne as candidates for the role of abelian envelope.
AB - For each integer t a tensor category V t is constructed, such that exact tensor functors V t - C classify dualizable t-dimensional objects in C not annihilated by any Schur functor. This means that V t is the “abelian envelope” of the Deligne category D t = Rep(GLt). Any tensor functor Rep(GLt) -C is proved to factor either through V t or through one of the classical categories Rep(GL(m|n)) with m - n = t. The universal property of V t implies that it is equivalent to the categories RepDt1 Dt2 (GL(X),), (t = t1 + t2, t1 not an integer) suggested by Deligne as candidates for the role of abelian envelope.
UR - http://www.scopus.com/inward/record.url?scp=85097847735&partnerID=8YFLogxK
U2 - https://doi.org/10.1093/IMRN/RNY144
DO - https://doi.org/10.1093/IMRN/RNY144
M3 - Article
SN - 1073-7928
VL - 2020
SP - 4602
EP - 4666
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 15
ER -