Александр Молев
Representations of the orthosymplectic Yangians
The Yangians form a remarkable family of quantum groups with a deep and substantive representation theory and numerous connections in mathematical physics. The Yangians admit at least three different presentations, including the R-matrix presentation going back to the work of Faddeev’s school in the 1980s. It is the R-matrix approach which turned out to be more suitable for the introduction of the super-versions of the Yangians as given by Nazarov (for the general linear Lie superalgebras, 1991) and Arnaudon et al. (for the orthosymplectic Lie superalgebras, 2003). The classification problem for simple finite-dimensional modules over the Yangians associated with the orthosymplectic Lie superalgebras osp(N|2m) with N=1,2,3 has been solved recently. We will discuss the solution which describes the representations in terms of their highest weights. Key arguments rely on Yangian odd reflections and an explicit construction of a family of elementary modules of the Yangian for osp(1|2).