Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 041, 28 pages      arXiv:1911.11842      https://doi.org/10.3842/SIGMA.2020.041
Contribution to the Special Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase for his 65th birthday

Generalized B-Opers

Indranil Biswas a, Laura P. Schaposnik b and Mengxue Yang b
a)  Tata Institute of Fundamental Research, India
b)  University of Illinois at Chicago, USA

Received November 28, 2019, in final form May 02, 2020; Published online May 14, 2020

Abstract
Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing and studying generalized $B$-opers (where ''$B$'' stands for ''bilinear''), obtained by endowing the underlying vector bundle with a bilinear form which is compatible with both the filtration and the connection. In particular, we study the structure of these $B$-opers, by considering the relationship of these structures with jet bundles and with geometric structures on a Riemann surface.

Key words: opers; connection; projective structure; Higgs bundles; differential operator; Lagrangians.

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