报告题目：A Difference Formula from Bethe/Gauge Correspondence and its Applications to Representation Theory and Completeness of Bethe Ansatz 

报告人：朱瑞东  苏州大学

报告时间：5月21日，14:00-15:00

报告地点：新楼312

摘要：

The Bethe/Gauge correspondence is a conjecture in mathematical physics, linking supersymmetric gauge theories to quantum integrable models. Quantum integtable models are a class of special quantum many-body systems, which are exactly solvable with the Bethe ansatz. A central mathematical challenge, however, is proving the completeness of the Bethe ansatz, i.e. whether all eigenstates are captured in this form.

Motivated by this problem and the Bethe/Gauge correspondence, we propose a universal difference formula in representation theory, which offers an efficient tool for computing tensor product multiplicities and branching rules. It is proven for Lie algebras, including type A (and also for types B, C, and D by the group of my collaborator, Peng Zhao). 

When applied to simple examples of A-type Lie superalgebras, it reproduces the counting of Bethe states in corresponding integrable spin chains. This provides a consistency check of the completeness of the Bethe ansatz in these models.