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Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators

Guner Muarem

SciPost Phys. Proc. 14, 038 (2023) · published 24 November 2023

Proceedings event

34th International Colloquium on Group Theoretical Methods in Physics


In this paper we use the canonical complex structure $\mathbb{J}$ on $\mathbb{R}^{2n}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold. Moreover, we prove that the algebra of these Dirac operators is isomorphic to the Lie algebra $\mathfrak{su}(1,2)$ which leads to the Howe dual pair $(U(n),\mathfrak{su}(1,2))$.

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