Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial super representations of the hyperalgebra of
  $\mathfrak{gl}_{m|n}$ at roots of unity   As a homomorphic image of the hyperalgebra $U_{q,R}(m|n)$ associated with the
quantum linear supergroup $U_\upsilon(\mathfrak{gl}_{m|n})$, we first give a
presentation for the $q$-Schur superalgebra $S_{q,R}(m|n,r)$ over a commutative
ring $R$. We then develop a criterion for polynomial supermodules of
$U_{q,F}(m|n)$ over a filed $F$ and use this to determine a classification of
polynomial irreducible supermodules at roots of unity. This also gives
classifications of irreducible $S_{q,F}(m|n,r)$-supermodules for all $r$. As an
application when $m=n\geq r$ and motivated by the beautiful work \cite{bru} in
the classical (non-quantum) case, we provide a new proof for the Mullineux
conjecture related to the irreducible modules over the Hecke algebra
$H_{q^2,F}({\mathfrak S}_r)$; see \cite{Br} for a proof without using the super
theory.

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th