AGT: Spin Leonard pairs and the proof of the Kresch-Tamvakis conjecture

Talk by Taiyo S. Terada.
In [Proc. Amer. Math. Soc. 152, 3, p. 1265] we proved a conjecture of Kresch & Tamvakis from 2001 about a certain 4F_3 hypergeometric series. In this talk, we discuss our proof of the conjecture and a related finding. Specifically, we construct a Leonard pair A, A* and a related sequence of matrices B_i. We identify the hypergeometric series in question with the eigenvalues of these matrices. We use the Biedenharn-Elliott identity to prove that the entries of the B_i are nonnegative. From this, we discuss two different arguments to derive the conjectured bound: one using the Perron-Frobenius theorem, and another using the theory of spin Leonard pairs.