A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and ...

It is shown that a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is semisimple and each irreducible admissible V -module is ordinary. A contravariant form on a Verma type admissible V -module is constructed and the radical is exactly the maximal proper submodule. As an application the rationality of V + L for any positive definite even lattice is obtained.

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and ...

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

The quantum α-determinant is defined as a parametric deformation of the quantum determinant. We investigate the cyclic Uq(sl2)-submodules of the quantum matrix algebra Aq(Mat2) generated by the powers of the quantum α-determinant. For such a cyclic module, there exists a collection of polynomials which describe the irreducible decomposition of it in the following manner: (i) each polynomial cor...

We investigate representations of the Z22-graded extension osp(1|2), which is spectrum generating algebra recently introduced version superconformal mechanics. The main result a classification irreducible lowest weight modules osp(1|2). This done via introduction Verma and its maximal invariant submodule generated by singular vectors. Explicit formulas all vectors are also presented.

Let R be an integral domain and let Q denote the quotient field of R. We investigate the structure of R-submodules of Q that are Q-irreducible, or completely Q-irreducible. One of our goals is to describe the integral domains that admit a completely Q-irreducible ideal, or a nonzero Q-irreducible ideal. If R has a nonzero finitely generated Q-irreducible ideal, then R is quasilocal. If R is int...