Abstract: The idea of organizing infinite families of combinatorial objects into graded vector spaces with an inductive structure (realized as a Hopf algebra) is a fundamental idea in algebraic combinatorics. However, one quickly encounters the problem of too much flexibility: what are the good bases?, what is the “right” inner product structure?, what are the best algebra morphisms on the space?, etc. One approach to making such choices more canonical is to associate the combinatorial Hopf algebra to the representation theory of some family of algebras (or, in our case, a tower of groups). This talk explores a combinatorial approach to making such a connection, illustrating the construction with several examples (involving Dyck paths, permutations and integer compositions, respectively).
This is joint work with F. Aliniaeifard.
A combinatorial approach to representation theory
03.05.2022 15:15 - 16:45
Organiser:
M. Drmota
Location:
TU Wien, Freihaus, Turm A, 8. Stock, Dissertantenraum