Zobrazeno 1 - 10
of 210
pro vyhledávání: '"COULEMBIER, KEVIN"'
Autor:
Coulembier, Kevin
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 determine what representations appear for certain examples of tens
Externí odkaz:
http://arxiv.org/abs/2406.00892
Autor:
Coulembier, Kevin, Flake, Johannes
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 proved to be a powerful tool in the ongoing classification of tensor c
Externí odkaz:
http://arxiv.org/abs/2405.19506
We study the number of indecomposable summands in tensor powers of the vector representation of SL2. Our main focus is on positive characteristic where this sequence of numbers and its generating function show fractal behavior akin to Mahler function
Externí odkaz:
http://arxiv.org/abs/2405.16786
Autor:
Coulembier, Kevin, Etingof, Pavel
We apply the recently introduced notion, due to Dyckerhoff, Kapranov and Schechtman, of $N$-spherical functors of stable infinity categories, which generalise spherical functors, to the setting of monoidal categories. We call an object $N$-bounded if
Externí odkaz:
http://arxiv.org/abs/2312.03972
Autor:
Coulembier, Kevin
We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.
Externí odkaz:
http://arxiv.org/abs/2311.02264
A symmetric tensor category $\mathcal D$ over an algebraically closed field $k$ is incompressible if every tensor functor out of $\mathcal D$ is an embedding. E.g., the categories $Vec$ and $sVec$ of (super)vector spaces are incompressible. Moreover,
Externí odkaz:
http://arxiv.org/abs/2306.09745
Autor:
Coulembier, Kevin
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some tensor categ
Externí odkaz:
http://arxiv.org/abs/2306.09727
Autor:
Coulembier, Kevin
We review some recent results on $K$-theory of perfection of commutative $\mF_p$-algebras and provide an alternative proof.
Externí odkaz:
http://arxiv.org/abs/2304.01421
Let G be a group and V a finite dimensional representation of G over an algebraically closed field k of characteristic p>0. Let $d_n(V)$ be the number of indecomposable summands of $V^{\otimes n}$ of nonzero dimension mod p. It is easy to see that th
Externí odkaz:
http://arxiv.org/abs/2301.09804
Publikováno v:
Algebr. Represent. Theory 27 (2024), no. 2, 1033-1062
In this paper we study the asymptotic behavior of the number of summands in tensor products of finite dimensional representations of affine (semi)group (super)schemes and related objects.
Comment: 21 pages, many figures, revision, comments welco
Comment: 21 pages, many figures, revision, comments welco
Externí odkaz:
http://arxiv.org/abs/2301.00885