nLab
Verma module

Given a semisimple Lie algebra 𝔤\mathfrak{g} over a field FF with Borel subalgebra 𝔟⊂𝔤\mathfrak{b}\subset\mathfrak{g} a Verma module is the induced module

U(𝔤)⊗ U(𝔟)F λ U(\mathfrak{g})\otimes_{U(\mathfrak{b})} F_\lambda

where F λF_\lambda is one dimensional representation of U(𝔟)U(\mathfrak{b}) corresponding to the character λ\lambda of 𝔟\mathfrak{b}.

This construction is used also for many other Lie algebras with triangular decomposition, for quantized enveloping algebras and many other generalizations.

Created on November 12, 2012 02:09:45 by Zoran Å koda (193.55.36.32)