Twisted Whittaker modules over U_(q)(gl_(n+1))

As is well known,the classical nonsingular Whittaker modules over quantum groups cannot be defined for the non-A1 type.In this paper,by choosing different generators for the quantum group U_(q)(gl_(n+1)),we introduce and study the twisted Whittaker modules over U_(q)(gl_(n+1)).We classify all the simple twisted Whittaker modules with nonsingular Whittaker functions.This agrees with Kostant’s results on Whittaker modules for the simple complex Lie algebras sln+1 as q approaches 1.

Simple Singular Whittaker Modules Over the Schrödinger Algebra

There are no simple singular Whittaker modules over most of important algebras,such as simple complex finite-dimensional Lie algebras,affine Kac-Moody Lie algebras,the Virasoro algebra,the Heisenberg-Virasoro algebra and the Schrödinger-Witt algebra.In this paper,however,we construct simple singular Whittaker modules over the Schrödinger algebra.Moreover,simple singular Whittaker modules over the Schrödinger algebra are classified.As a result,simple modules for the Schrödinger algebrawhich are locally finite over the positive part are completely classified.We also give characterizations of simple highestweight modules and simple singular Whittaker modules.

Whittaker modules over loop Virasoro algebra

In this paper, we study Whittaker modules over the loop Virasoro algebra relative to some total order. We give a description of all Whittaker vectors for the universal Whittaker modules. We also show that any universal Whittaker module admits a unique simple quotient modules except for a special case.

Whittaker Modules for the Derivation Lie Algebra of Torus with Two Variables

Let L be the derivation Lie algebra of C[t1^±1 , t2^±1 ]. Given a triangle decomposition L = L＋ η ＋ L-, we define a nonsingular Lie algebra homomorphism φ ： L＋ → C and the universal Whittaker L-module We of type φ. We obtain all Whittaker vectors and submodules of We. Moreover, all simple Whittaker L-modules of type φ are determined.

Classification on irreducible Whittaker modules over quantum group Uq(sl3,∧)

We define the Whittaker modules over the simply-connected quantum group U_(q)(sl3,∧),where A is the weight lattice of Lie algebra sl3.Then we completely classify all those simple ones.Explicitly,a simple Whittaker module over U_(q)(sl3,∧)is either a highest weight module,or determined by two parameters z∈C andγ∈C^(*)(up to a Hopf automorphism).

Imaginary Modules over the Affine Nappi-Witten Algebra

In this paper,we consider the imaginary highest weight modules and the imaginary Whittaker modules for the affine Nappi-Witten algebra.We show that simple singular imaginary Whittaker modules at level(κ、c)(κ∈C~*)are simple imaginary highest weight modules.The necessary and sufficient conditions for these imaginary modules to be simple are given.All simple imaginary modules are classified.

Non-weight modules over the mirror Heisenberg-Virasoro algebra

In this paper,we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra D,including Whittaker modules,U(Cd_(0))-free modules and their tensor products.More precisely,we give the necessary and sufficient conditions for the Whittaker modules to be irreducible.We determine all the D-module structures on U(Cd_(0)),and find the necessary and sufficient conditions for these modules to be irreducible.At last,we determine the necessary and sufficient conditions for the tensor products of Whittaker modules and U(Cd_(0))-free modules to be irreducible,and obtain that any two such tensor products are isomorphic if and only if the corresponding Whittaker modules and U(Cd_(0))-free modules are isomorphic.These lead to many new irreducible non-weight modules over D.