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

Autor:	Muarem, Guner
Rok vydání:	2022
Předmět:	Mathematics - Representation Theory Mathematical Physics Mathematics - Complex Variables Mathematics - Symplectic Geometry
Druh dokumentu:	Working Paper
Popis:	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 $(\mathsf{U}(n),\mathfrak{su}(1,2))$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.16640 Zobrazit plný text záznamu View this record from Arxiv