安德烈·利亚希克 , 尼古拉·莱舍提金 , 许睿捷

Daniil Sarafannikov

2026年10月12日 15:30 至 16:30

A7-201

S. Arthamonov and Sh. Shakirov introduced three commuting q-difference operators on symmetric Laurent polynomials in three variables, attached to curves on a closed surface of genus two. Their joint eigenfunctions are the genus two Macdonald polynomials. Whether these polynomials are orthogonal for some scalar product was not known. We study categories of finite-dimensional graded representations of the loop superalgebra of a degeneration of the exceptional Lie superalgebra D(2|1,α). We construct three endofunctors of the derived category whose classes in the Grothendieck group are the operators of Arthamonov and Shakirov. The commutativity of these operators lifts to an isomorphism of functors. The endofunctors are self-adjoint with respect to the Ext pairing. Hence the pairing induced on the Grothendieck group makes the operators self-adjoint and the genus two Macdonald polynomials orthogonal.