论文标题
费尔米金和玻色子代数以及相关狄拉克操作员的单一二重性
Unitary Howe dualities for fermionic and bosonic algebras and related Dirac operators
论文作者
论文摘要
在本文中，我们使用$ \ mathbb {r}^{2n} $上的规范复杂结构$ \ mathbb {j} $引入Symbletic Dirac Operator的转换。事实上，这些操作员可以被解释为狄拉克操作员在Hermitian歧管上的骨气类似物。此外，我们证明了这些符号DIRAC运算符的代数对Lie代数$ \ Mathfrak {su}（1,2）$是同构，它导致Howe Dual Pair Pair $（\ Mathsf {u}（U}（u}（n）（n），\ Mathfrak {su}（su}（1,1,2））$。
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 $(\mathsf{U}(n),\mathfrak{su}(1,2))$.
