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Unitary Howe dualities for fermionic and bosonic algebras and related Dirac operators
- Publication Year :
- 2022
-
Abstract
- In this paper we use the canonical complex structure $\mathbb{J}$ on $\mathbb{R}^{2n}$ to introduce a twist of the symplectic Dirac operator. As a matter of fact, these operators can be interpreted as the bosonic analogues of the Dirac operators on a Hermitian manifold. Moreover, we prove that the algebra of these symplectic Dirac operators is isomorphic to the Lie algebra $\mathfrak{su}(1,2)$ which leads to the Howe dual pair $(\mathsf{U}(n),\mathfrak{su}(1,2))$.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2211.16640
- Document Type :
- Working Paper