Beijing Institute of Mathematical Sciences and Applications

Semen Artamonov , Yevgen Makedonskyi , Pavel Nikitin , Shamil Shakirov

Yevgen Makedonskyi

Friday, September 11, 2026 1:00 PM - 2:30 PM

A3-2a-302

Zoom 361 038 6975 (BIMSA)

S. Arthamonov and Sh. Shakirov introduced three commuting operators O_{ij}, i=1,2,3 on the algebra of symmetric polynomials \mathbb{Z}((q,t))[x_1,x_2,x_3]. Their joint eigenvectors are called rank 2 MacDonald polynomials. It was unknown is thee a scalar product which makes these polynomials orthogonally. We study the category of representations of Lie superalgebra constructed from the exceptional superalgebra D(2|1,\alpha). We construct three endofunctors on this category, whose action on the Grothendieck group coincide with O_{ij}. These endofunctors are orthogonal with respect to Ext pairing. Using this property we get that the shadow of this pairing on the Grothendieck group makes MacDonald polynomials orthogonal

Ievgen Makedonskyi obtained a PhD degree in mathematics from the Russian University of Advanced Economic Research and then worked at the Russian University of Advanced Economic Research, the Max Planck Institute of Mathematics, the University of Tokyo, Skolkovo University of Science and Technology, and Jena University in Germany. In 2022, he joined the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications as an assistant professor. His research interests include Lie algebra, polynomial derivation, affine Kac Moody Lie algebra, Weyl and Demazure module Asymmetric Macdonald polynomials, recent algebras, arc varieties, etc.