Classical Yang-Baxter equation and sheaves on degenerations of elliptic curves

• Applicant: Professor Dr. Igor Burban
• Subject Area: Mathematics
• Term: from 2012 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 219669121

We want to relate solutions of CYBE with simple torsion free coherent sheaveson curves of arithmetic genus one.1. Let Kp be the configuration of p generic concurrent projective lines in Pp-1 forp ≥ 3. We are going to studya) simple vector bundles on Kp,b) solutions of CYBE attached to the corresponding universal families,c) related algebraic structures: Frobenius functionals on seawead Lie algebras, representations of a bocses arising in the study of vector bundles on Kp etc.2. Establish a link between these results with problems of mathematical physics.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory