Abstract: Characters of the irreducible polynomial representations of the general linear groups over the complex numbers are given by Schur polynomials. Several determinantal formulae for the Schur polynomials are known such as the Jacobi-Trudi formula, its dual (the Nägelsbach-Kostka formula) and the Giambelli formula. Analogous formulae hold for the symplectic and the orthogonal groups. These can be shown by using lattice path descriptions of tableaux as done by Markus Fulmek and Christian Krattenthaler in a paper of 1997 where they used various different tableaux models defined by King, Proctor, Sundaram as well as King and Welsh. In the case of ordinary Schur polynomials, determinantal formulae are also known for Schur polynomials indexed by partitions of skew shape. However, the skew analogues of symplectic and orthogonal characters have received very little attention so far.
In this talk, we close this gap by presenting (dual) Jacobi-Trudi-type and Giambelli-type formulae for skew analogues of symplectic and (even and odd) orthogonal characters. We achieve this by using lattice path descriptions of tableaux defined by Koike and Terada.
This is joint work with Seamus Albion, Ilse Fischer and Florian Schreier-Aigner.