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A Hermitian refinement of symplectic Clifford analysis
David Eelbode, Guner Muarem
In this paper we develop the Hermitian refinement of symplectic Clifford analysis, by introducing a complex structure on the canonical symplectic manifold $(\mathbb {R…
Branching symplectic monogenics using a Mickelsson--Zhelobenko algebra
David Eelbode, Guner Muarem
In this paper we consider (polynomial) solution spaces for the symplectic Dirac operator (with a focus on -homogeneous solutions). This space forms an infinite-dimensional repre…
Unitary Howe dualities for fermionic and bosonic algebras and related Dirac operators
Guner Muarem
In this paper we use the canonical complex structure on to introduce a twist of the symplectic Dirac operator. As a matter of fact, these operators c…
The orthogonal branching problem for symplectic monogenics
David Eelbode, Guner Muarem
In this paper we study the sp(2m)-invariant Dirac operator Ds which acts on symplectic spinors, from an orthogonal point of view. By this we mean that we will focus on the subalgeb…