Bases for some reciprocity algebras II

Howe, Roger; Lee, Soo Teck

doi:10.1016/j.aim.2005.08.006

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Cited by 6 publications

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“…Then the decomposition in the Corollary above can be regarded as an explicit form of the branching rules under the reduction of the symmetry from Spin(m) to Spin(p) × Spin(q). It can be compared with the general results presented in [17].…”

Section: Theorem 12mentioning

confidence: 99%

Orthogonal basis for spherical monogenics by step two branching

2011

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Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R m . They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on R m . Fix the direct sum R m = R p ⊕ R q . In this paper we will study the decomposition of the space Mn(R m , Cm) of spherical monogenics of order n under the action of Spin(p)×Spin(q). As a result we obtain a Spin(p)× Spin(q)-invariant orthonormal basis for Mn(R m , Cm). In particular, using the construction with p = 2 inductively, this yields a new orthonormal basis for the space Mn(R m , Cm).Mathematics Subject Classification. 30G35, 33C45, 22E70.

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Section: Theorem 12mentioning

confidence: 99%