Authors: E. Cline, B. Parshall, and L. Scott

Title: On $\Ext$-transfer for algebraic groups

Abstract: This paper builds upon the work of Cline and Donkin to
describe  explicit equivalences between some categories associated
to the category of rational modules for a reductive group $G$ and
categories associated to the category of rational modules for a
Levi subgroup $H$. As an application, we establish an
$\Ext$-transfer result from rational $G$-modules to rational
$H$-modules. In case $G=GL_n$, these results can be illustrated in
terms of classical Schur algebras. In that case, we establish
another category equivalence, this time between the module
category for a Schur algebra and the module category for a union
of blocks for a natural quotient of a larger Schur algebra. This
category equivalence provides a further $\Ext$-transfer theorem
from the original Schur algebra to the larger Schur algebra.  This
result, announced in earlier work of Parshall-Scott (Proc. LMS, in
press), extends to the category level the decomposition number
method of Erdmann. Finally, we indicate (largely without proof)
some natural variations to situations involving quantum groups and
$q$-Schur algebras.


Status: Paper has appeared in  "Transformation Groups", vol. 9,
No. 3 (2004), 213--236

        New stuff: A very brief sketch attached at end of paper on
        the connections of this work with recent work of W.
        Turner.