0 M ar 2 01 2 On Shift Spaces with Algebraic Structure ⋆

ar X iv : m at h - ph / 0 31 10 01 v 4 3 N ov 2 00 4 Clifford Valued Differential Forms , Algebraic Spinor Fields

ar X iv : 0 80 4 . 15 97 v 2 [ m at h . FA ] 1 5 O ct 2 00 8 INVARIANCE OF A SHIFT - INVARIANT SPACE

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are...

ar X iv : 0 80 4 . 15 97 v 3 [ m at h . FA ] 2 1 D ec 2 00 8 INVARIANCE OF A SHIFT - INVARIANT SPACE

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-invariant subspaces S that are also invariant under additional (non-integer) translations. For the case of finitely generated spaces, these spaces are...

ar X iv : m at h - ph / 0 31 10 01 v 3 6 O ct 2 00 4 Clifford Valued Differential Forms , Algebraic Spinor Fields , Gravitation , Electromagnetism and ” Unified ” Theories ∗

ar X iv : 0 80 6 . 01 70 v 2 [ m at h . Q A ] 1 J ul 2 00 8 WEIGHT MULTIPLICITY POLYNOMIALS OF MULTI - VARIABLE WEYL MODULES

This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable cases and discuss the underlying combinatorics.