An explicit formula for the canonical bilinear form on Grothendieck ring of Lie supergroup G L ( n , m ) is given. As an application we get algorithm decomposition Euler characters in terms irreducible modules category partially polynomial modules.

The Jordan canonical form parametrises similarity classes in the nilpotent cone Nn, consisting of n× n nilpotent complex matrices, by partitions of n. Achar and Henderson (2008) extended this and other well-known results about Nn to the case of the enhanced nilpotent cone C ×Nn. 1. Jordan canonical form The Jordan canonical form (JCF), introduced in 1870 [10], is one of the most useful tools in...

In this paper, we derive a canonical representation for the first order hyperbolic equation systems with their coefficient matrices satisfying the Clifford algebra Cl(1, 3), and then demonstrate some of its applications. This canonical formalism can naturally give a unified description for the fundamental fields in physics. PACS numbers: 11.10.-z, 11.10.Cd, 12.10.-g

We derive the complete (curvature) terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the o(α′ ) corrections to string scattering amplitudes, and are consistent with duality conjectures. In the particular case of the D3-brane with trivial normal bundle, considerations ...