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.

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).

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.

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.

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.