Based on the representation of a set of canonical operators on the lattice , which are Clifford-vector-valued, we will introduce new families of special functions of hypercomplex variable possessing symmetries. The Fourier decomposition of the space of Clifford-vector-valued polynomials with respect to the – module gives rise to the construction of new families of polynomial sequences as eigenfunctions of a coupled system involving forward/backward discretizations of the Euler operator .

Moreover, the interpretation of the one-parameter representation of the Lie group as a semigroup will allows us to describe the polynomial solutions of a homogeneous Cauchy problem on involving the differencial-difference operator .

**arXiv preprint:** http://arxiv.org/abs/1304.7191v2

**Related arXiv preprints:**

*(Discrete) Almansi Type Decompositions: An umbral calculus framework based on symmetries*–http://arxiv.org/abs/1102.5434.*Fischer Decomposition for Difference Dirac Operators*–http://arxiv.org/abs/math/0609823.

**Related posts:**

- Flashback-”On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices”
- New families of Special Functions on the lattice within Hypercomplex Variables-In Preparation.

Hi Nelson, really like your blog. I’m doing research on discrete spacetimes – that’s how I found your blog. Alot of the stuff here looks useful and interesting – I can see I’m going to need to review the whole blog. Please feel free to visit my research blog at http://quantumtetrahedron.wordpress.com/

– any feedback or comments are welcome.

Hi David,

Many thanks for your comment. Currently I am start working on Feynman diagrams in interrelationship with quantization of discrete spacetimes. Maybe we must keep in touch by e-mail.

Soon,

Nelson