Taika Okuda
Explicit Formulae for Deformation Quantization with Separation of Variables of $G_{2,4}(\mathbb{C})$
This is the joint work with Akifumi Sako (Tokyo University of Science). We will talk about the explicit formula that gives the deformation quantization with separation of variables of $G_{2,4}(\mathbb{C})$. For arbitrary locally symmetric Kähler manifolds, the construction methods of deformation quantization with separation of variables of it were proposed by Sako-Suzuki-Umetsu and Hara-Sako. These constructions make it possible to give the star product on a locally symmetric Kähler manifold such that its coefficients satisfy some recurrence relations. The explicit star product for $\mathbb{C}^N$, $\mathbb{C}P^N$, $\mathbb{C}H^N$ and arbitrary one- and two-dimensional ones were obtained from this construction method so far. In this talk, we denote the explicit formula of the star product on $G_{2,4}(\mathbb{C})$ by using the construction method proposed by Hara-Sako. We show that for $G_{2,4}(\mathbb{C})$, the explicit form of general terms of the recurrence relations given by Hara-Sako can be determined explicitly via the Fock representations. From the obtained general terms, we also give the star product on \(G_{2,4}(\mathbb{C})\) explicitly.
