Speaker
岡田聡一 (名古屋大学多元数理科学研究科)
Date
October 7, 14:45-15:35
Title
Intermediate symplectic characters and applications (slide)
Abstract
The intermediate symplectic characters, introduced by R. Proctor, interpolate between Schur functions and symplectic characters. They arise as the characters of indecomposable representations of the intermediate symplectic group, which is defined as the group of linear transformations fixing a (not necessarily non-degenerate) skew-symmetric bilinear form. In this talk, we present Jacobi-Trudi-type determinant formulas and bialternant formulas for intermediate symplectic characters. Also we give two applications of the bialternant formula. One is a linear algebraic proof to an odd symplectic character identity, which was found by R. P. Brent, C. Krattenthaler and S. O. Warnaar. The other is a proof and variations of the Hopkins-Lai's product formula for the number of shifted plane partitions of double-staircase shape with bounded entries.