Abstract
Based on the Brieskorn-Slodowy-Grothendieck diagram, we write the holomorphic
structures (or filtrations) of the ADE Lie algebra bundles over the
corresponding type ADE flag varieties, over the cotangent bundles of these flag
varieties, and over the corresponding type $ADE$ singular surfaces. The main
tool is the cohomology of line bundles over flag varieties and their cotangent
bundles.
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