Computations of sheaves associated to the representation theory of sl_2

TL;DR

This paper explicitly computes sheaves related to the representation theory of sl_2, including kernels and functors for indecomposable modules, providing concrete examples and a review of module classification.

Contribution

It provides explicit calculations of sheaves associated with sl_2 representations, including kernels and functors, and reviews the module classification and sheaf theory for restricted Lie algebras.

Findings

Computed rm rm rm for all indecomposable modules

Determined F_i(M) for indecomposable Weyl modules when i e7 p

Reviewed classification of sl_2-modules and sheaf theory for restricted Lie algebras

Abstract

We explicitly compute examples of sheaves over the projectivization of the spectrum of the cohomology of sl_2. In particular, we compute \ker\Theta_M for every indecomposable M and we compute F_i(M) when M is an indecomposable Weyl module and i \neq p. We also give a brief review of the classification of sl_2-modules and of the general theory of such sheaves in the case of a restricted Lie algebra.