Seminar on Combinatorics, Lie Theory, and Topology
# Baxter Q-operators, QQ-systems and the shifted Yangian

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Aula Magna (Department of Mathematics)
### Aula Magna

#### Department of Mathematics

Description

I plan to discuss the construction of Baxter Q-operators within the framework of the Quantum Inverse Scattering Method. The method follows the standard procedure for the transfer matrix construction of spin chains that was developed by Faddeev and collaborators but employs Lax matrices with an infinite-dimensional auxiliary space. Those Lax matrices do not fit into the standard Yangian of Drinfeld but can be understood in the context of the shifted Yangian. The Q-operators satisfy a set of functional relations that are known as QQ-relations that can be seen as the successor of the famous Bethe equations. In the case of the Yangian of $\mathsf{su}(n)$, the full set of functional relations can be derived from the Q-operators. Beyond $\mathsf{su}(n)$ new obstacles arise in the construction of Q-operators which will be discussed in the example of $\mathsf{so}(2r)$.