OIST Representation Theory Seminar
Soichi Okada, Nagoya University
Title: Intermediate symplectic characters and enumeration of shifted plane partitions
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. By using the bialternant formula, we can derive factorization formulas for sums of intermediate symplectic characters, which allow us to give a proof and variations of Hopkins' conjecture on the number of shifted plane partitions of double-staircase shape with bounded entries.