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 - Funding Information: This work was supported by Israel Science Foundation [446/15 to V.H.] and National Science 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

ER -