The Robinson-Schensted-Knuth (RSK) correspondence is a combinatorial bijection between matrices with non-negative integer entries and pairs of semistandard Young tableaux of the same shape. This result is central to the representation theory of the symmetric group. Indeed, by keeping track of certain weights on both the matrices and the tableaux, we can recover the Cauchy identity, which has a number of non-trivial consequences. For the third part of the interview, I intend to present a recent result of mine on the combinatorics of Smirnov words, and its connections with the theory of diagonal coinvariants. I plan to give an introduction to the theory of symmetric functions and Macdonald eigenoperators, and then give a sketch of the proof of the result. While the first part is intended to be introductory, the second part will be elementary, and I hope that most of it will be accessible to a broad audience. Title and abstract follows.
The Robinson-Schensted-Knuth correspondence
22.05.2024 09:00 - 09:20
Organiser:
Fakultät für Mathematik, Dekan Radu Ioan Boţ
Location: