7 papers
Generalized polynomial functors
Jonathan D. Axtell
We define Schur categories, , associated to a -linear category , over a commutative ring . The corresponding representation categories, $\…
Cellularity of generalized Schur algebras via Cauchy decomposition
Jonathan D. Axtell
We describe a generalization of Hashimoto and Kurano's Cauchy filtration for divided powers algebras. This filtration is then used to provide a cellular structure for generalized S…
Quantum generalized Kac--Moody algebras via Hall algebras of complexes
Jonathan D. Axtell, Kyu-Hwan Lee
We establish an embedding of the quantum enveloping algebra of a symmetric generalized Kac--Moody algebra into a localized Hall algebra of -graded complexes of represe…
On Schur Superfunctors
Jonathan Axtell
We introduce super-analogues of the Schur functors defined by Akin, Buchsbaum and Weyman. These {\em Schur superfunctors} may be viewed as characteristic-free analogues of the fini…
Spin polynomial functors and representations of Schur superalgebras
Jonathan Axtell
We introduce categories of homogeneous strict polynomial functors, $\Pol^\I_{d,\k}$ and $\Pol^\II_{d,\k}$, defined on vector superspaces over a field $\k$ of characteristic not equ…
Vertex Operator Algebras Associated to Type G Affine Lie Algebras II
Jonathan Axtell
We continue the study of the vertex operator algebra associated to a type affine Lie algebra at admissible one-third integer levels, $k = -2 + m + \tfrac{i}{3}…
Vertex Operator Algebras Associated to Type G Affine Lie Algebras
Jonathan D. Axtell, Kyu-Hwan Lee
In this paper, we study representations of the vertex operator algebra at one-third admissible levels for the affine algebra of type . We…