arXiv 2211.166402022-11math.RTmath-phmath.CVmath.MPmath.SG

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

Guner Muarem

英文摘要：

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 $(\mathsf{U}(n),\mathfrak{su}(1,2))$.

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