Whittaker modules for the derivation Lie algebra of torus with two variables

Abstract

Let L be the derivation Lie algebra of C[t ±1 1 , t ±1 2 ]. Given a triangle decomposition L = L + ⊕ h ⊕ L − , we define a nonsingular Lie algebra homomorphism ψ : L + → C and the universal Whittaker L-module W ψ of type ψ. We obtain all Whittaker vectors and submodules of W ψ , and all simple Whittaker L-modules of type ψ.

Representations of Generalized Loop Planar Galilean Conformal Algebras W(Γ)

“…In particular, the Whittaker modules and U(h)-free modules have been widely studied for many Lie algebras. The Whittaker modules for many other Lie algebras have been investigated, such as in reference [19][20][21][22][23][24][25][26][27]. The Whittaker modules for the affine Lie algebra A…”