Self Extensions of Simple Modules over Semisimple Lie Algebras

Abstract

A categorical framework is provided, where most of the properties of the celebrated category 𝒪 (introduced by Bernstein, Gelfand, and Gelfand in [1]) are preserved but, for each simple object S, the dimension of Ext ¹(S, S) no longer needs to be zero. A combinatorial description of such numbers is given and, consequently, a full description of all quivers corresponding to blocks of representations is obtained.

Key Words:

• Ext spaces
• Verma modules
• Semisimple Lie algebras

2010 Mathematics Subject Classification:

• 17B10
• 16G20

Notes

Communicated by J. Alev.