TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.038
TI  - Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators
PY  - 2023/11/24
UR  - https://scipost.org/SciPostPhysProc.14.038
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 038
A1  - Muarem, Guner
AB  - 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 $(U(n),\mathfrak{su}(1,2))$.
ER  -

@Article{10.21468/SciPostPhysProc.14.038,
	title={{Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators}},
	author={Guner Muarem},
	journal={SciPost Phys. Proc.},
	pages={038},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.038},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.038},
}