20 citations · 53 across the 15 of their papers we have counts for
11 papers · 1 filter
The universal property of strict polynomial functors
Antoine Touzé
In characteristic zero, the category of strict polynomial functors is well-known to be the tensor abelian category freely generated by one object. We show that this property fails…
Décompositions à la Steinberg sur une catégorie additive
Aurélien Djament, Antoine Touzé, Christine Vespa
We give a description of simple functors taking finitely generated values, from a small additive category to the category of vector spaces over a field. This result is analogous to…
Connectedness of cup products for polynomial representations of and applications
Antoine Touzé
We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this res…
A functorial control of integral torsion in homology
Antoine Touzé
We study the integral torsion of the values of strict polynomial functors defined over the integers. We interpret some classical homological invariants as values of strict polynomi…
Polynomial functors and categorifications of Fock space
Jiuzu Hong, Antoine Touzé, Oded Yacobi
Fix an infinite field of characteristic , and let $\g$ be the Kac-Moody algebra if and otherwise. Let $\PP$ denote the…
A construction of the universal classes for algebraic groups with the twisting spectral sequence
Antoine Touzé
In this article, we apply some ideas developped by M. Chałupnik to the framework of strict polynomial bifunctors. This allows us to get a new proof of the existence of the `univers…
Ringel duality and derivatives of non-additive functors
Antoine Touzé
We prove that Ringel duality in the category of strict polynomial functors can be interpreted as derived functors of non-additive functors (in the sense of Dold and Puppe). We give…
Bar complexes and extensions of classical exponential functors
Antoine Touzé
We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and br…
Cohomology of classical algebraic groups from the functorial viewpoint
Antoine Touzé
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for gene…
Bifunctor cohomology and Cohomological finite generation for reductive groups
Antoine Touzé, Wilberd van der Kallen
Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant the…
Universal classes for algebraic groups
Antoine Touzé
We exhibit cocycles representing certain classes in the rational cohomology of of the general linear group with coefficients in the divided powers of a Frobenius twist of the adjoi…