Abstract: I will present some beautiful connections between combinatorics and the representation theory of the symmetric group.  Starting with an algorithmic way to obtain the longest increasing subsequence of a permutation, we discover the famous Robinson-Schensted correspondence. This is a bijection between permutations and pairs of combinatorial objects, called standard Young tableaux.

We then shift gears to the representation theory of the symmetric group. After recalling the basic definitions, we focus on describing its irreducible representations. We will see that these are indexed by integer partitions. More interestingly, the number of standard Young tableaux for a given partition is precisely the dimension of the corresponding irreducible representation.  In this light, we can interpret the Robinson-Schensted correspondence as a bridge between combinatorics and representation theory.

Der Link zum Vortrag wird auf der Website unter www.vsmath.at/academics/phd-colloquia veröffentlicht.