Combinatorial parameters and group representations

This survey talk will be focused on the interplay
between presentations and representations (of classical Weyl
groups and other closely related groups) and combinatorial
identities on these groups.

The motto is to expose hidden algebraic properties and
representation theoretic interpretations of classical parameters.
For example, combinatorial parameters and identities on
permutations may be interpreted within symmetric group
representations. These interpretations may serve as criteria for
“good” extensions of identities to other groups.