Hans Höngesberg: Skew symplectic and orthogonal characters through lattice paths

Date of publication: 24. 5. 2024
Discrete mathematics seminar
Plemljev seminar, Jadranska 19

Abstract: Symmetric functions play a central role in algebraic combinatorics, chief among them the (skew) Schur functions. These symmetric functions admit many determinantal expressions such as the Jacobi-Trudi or Giambelli identities. Comparatively, the skew symplectic and orthogonal Schur functions have received very little attention in this direction.

In this talk, I will establish analogues of the classical determinantal formulas for these characters. The approach is entirely combinatorial, using several (standard) methods in lattice path combinatorics. I will also explain all the basic definitions regarding symmetric functions and tableaux combinatorics.

This is joint work with Seamus Albion, Ilse Fischer and Florian Schreier-Aigner.