Since their introduction by Beilinson–Drinfeld (Opers, 1993. arXiv math/0501398; Quantization of Hitchin’s integrable system and Hecke eigensheaves, 1991), opers have seen several generalizations. In Biswas et al. (SIGMA Symmetry Integr Geom Methods Appl 16:041, 2020), a higher rank analog was studied, named generalized B-opers, where the successive quotients of the oper filtration are allowed to have higher rank and the underlying holomorphic vector bundle is endowed with a bilinear form which is compatible with both the filtration and the oper connection. Since the definition did not encompass the even orthogonal groups, we dedicate this paper to study generalized B-opers whose structure group is \(\mathrm{SO}(2n,{\mathbb {C}})\) and show their close relationship with geometric structures on a Riemann surface.

自从Beilinson-Drinfeld (Opers, 1993. arXiv math/0501398; Quantization of Hitchin's integrable system and Hecke eigensheaves, 1991) 引入它们以来，opers 已经看到了一些概括。在比斯瓦斯等人。(SIGMA Symmetry Integr Geom Methods Appl 16:041, 2020)，研究了一个更高阶的类似物，称为广义B- opers，其中允许 oper 过滤的连续商具有更高的秩，并且底层全纯向量丛被赋予与过滤和操作连接兼容的双线性形式。由于定义不包括偶数正交基团，我们致力于本文研究广义乙-opers其结构基团是\（\ mathrm {SO}（2N，{\ mathbb {C}}）\） 并展示它们与黎曼曲面上的几何结构的密切关系。