A Verma module is a highest-weight module for a complex semisimple Lie algebra. Given a Cartan
subalgebra 
,
a Borel subalgebra 
containing 
, and a weight 
, the Verma module is the induced module
 |
where 
denotes the universal enveloping algebra
and 
is the one-dimensional 
-module on which 
acts by 
and the nilpotent radical of 
acts by zero. Every highest-weight module
of highest weight 
is a quotient module
of 
, and 
has a unique irreducible quotient
module.
