2000 character limit reached
On the composition structure of the twisted Verma modules for $\mathfrak{sl}(3,\mathbb{C})$ (1509.00646v1)
Published 2 Sep 2015 in math.RT, math.AP, and math.FA
Abstract: We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra $\mathfrak{sl}(3, \mathbb{C})$, including the explicit structure of singular vectors for both $\mathfrak{sl}(3, \mathbb{C})$ and one of its Lie subalgebras $\mathfrak{sl}(2, \mathbb{C})$, and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as $\mathrm{{D}}$-modules on the Schubert cells in the full flag manifold for $\mathrm{SL}(3, \mathbb{C})$.