A Crystal-Basis Approach to the Littlewood-Richardson Rule
Time: 2026-05-27
Published By: He Liu
Speaker(s): Shaolong Han (BICMR)
Time: 15:00-16:00 May 29, 2026
Venue: Room 78301, Jingchunyuan 78, BICMR
The Littlewood-Richardson rule is a central result in representation theory and algebraic combinatorics, describing tensor product decompositions and products of Schur polynomials. This talk presents the rule from the viewpoint of crystal bases. Beginning with $U_q(\mathfrak{sl}_2)$, I will explain how crystal graphs encode the combinatorial structure of representations in the limit $q\to 0$. I will then discuss crystal bases for $U_q(\mathfrak{sl}_n)$, their realization by semistandard Young tableaux, and the interpretation of Littlewood-Richardson coefficients as counting highest weight elements in tensor products of crystals.
