Semi-infinite highest weight categories
J Brundan, C Stroppel - arXiv preprint arXiv:1808.08022, 2018 - arxiv.org
We develop axiomatics of highest weight categories and quasi-hereditary algebras in order
to incorporate two semi-infinite situations which are in Ringel duality with each other; the …
to incorporate two semi-infinite situations which are in Ringel duality with each other; the …
New incompressible symmetric tensor categories in positive characteristic
We propose a method of constructing abelian envelopes of symmetric rigid monoidal
Karoubian categories over an algebraically closed field k. If char (k)= p> 0, then we use this …
Karoubian categories over an algebraically closed field k. If char (k)= p> 0, then we use this …
Monoidal abelian envelopes
K Coulembier - Compositio Mathematica, 2021 - cambridge.org
We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal
categories. This establishes a new tool for the construction of tensor categories. As an …
categories. This establishes a new tool for the construction of tensor categories. As an …
Commutative algebra in tensor categories
K Coulembier - arXiv preprint arXiv:2306.09727, 2023 - arxiv.org
We develop some foundations of commutative algebra, with a view towards algebraic
geometry, in symmetric tensor categories. Most results establish analogues of classical …
geometry, in symmetric tensor categories. Most results establish analogues of classical …
Monoidal abelian envelopes with a quotient property
We study abelian envelopes for pseudo-tensor categories with the property that every object
in the envelope is a quotient of an object in the pseudo-tensor category. We establish an …
in the envelope is a quotient of an object in the pseudo-tensor category. We establish an …
Inductive systems of the symmetric group, polynomial functors and tensor categories
K Coulembier - arXiv preprint arXiv:2406.00892, 2024 - arxiv.org
We initiate the systematic study of modular representations of symmetric groups that arise
via the braiding in (symmetric) tensor categories over fields of positive characteristic. We …
via the braiding in (symmetric) tensor categories over fields of positive characteristic. We …
The periplectic Brauer algebra
K Coulembier - Proceedings of the London Mathematical …, 2018 - Wiley Online Library
We study the periplectic Brauer algebra introduced by Moon in the study of invariant theory
for periplectic Lie superalgebras. We determine when the algebra is quasi‐hereditary, when …
for periplectic Lie superalgebras. We determine when the algebra is quasi‐hereditary, when …
Towards higher Frobenius functors for symmetric tensor categories
K Coulembier, J Flake - arXiv preprint arXiv:2405.19506, 2024 - arxiv.org
We develop theory and examples of monoidal functors on tensor categories in positive
characteristic that generalise the Frobenius functor from\cite {Os, EOf, Tann}. The latter has …
characteristic that generalise the Frobenius functor from\cite {Os, EOf, Tann}. The latter has …
Deligne categories and the periplectic Lie superalgebra
I Entova-Aizenbud, V Serganova - arXiv preprint arXiv:1807.09478, 2018 - arxiv.org
We study stabilization of finite-dimensional representations of the periplectic Lie
superalgebras $\mathfrak {p}(n) $ as $ n\to\infty $. The paper gives a construction of the …
superalgebras $\mathfrak {p}(n) $ as $ n\to\infty $. The paper gives a construction of the …
The periplectic Brauer algebra III: the Deligne category
K Coulembier, M Ehrig - Algebras and Representation Theory, 2021 - Springer
We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on
the periplectic analogue of Deligne's universal monoidal category. We use the …
the periplectic analogue of Deligne's universal monoidal category. We use the …