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Spaces of spinor‐valued homogeneous polynomials, and in particular spaces of spinor‐valued spherical harmonics, are decomposed in terms of irreducible representations of the symplectic group Sp( p ). These Fischer decompositions involve spaces of homogeneous, so‐called   o  s  p  (  4  |  2  )  ‐monogenic polynomials, the Lie super algebra   o  s  p  (  4  |  2  )   being the Howe dual partner to the symplectic group Sp( p ). In order to obtain Sp( p )‐irreducibility, this new concept of   o  s  p  (  4  |  2  )  ‐monogenicity has to be introduced as a refinement of quaternionic monogenicity; it is defined by means of the four quaternionic Dirac operators, a scalar Euler operator   E   underlying the notion of symplectic harmonicity and a multiplicative Clifford algebra operator  P  underlying the decomposition of spinor space into symplectic cells. These operators   E   and  P , and their Hermitian conjugates, arise naturally when constructing the Howe dual pair   o  s  p  (  4  |  2  )  ×  Sp  (  p  )  , the action of which will make the Fischer decomposition multiplicity free. Copyright © 2016 John Wiley & Sons, Ltd.

Fischer decomposition for o s p ( 4 | 2 ) ‐monogenics in quaternionic Clifford analysis