Littlewood-Richardson coefficients: Reduction formulae and a conjecture by King, Tollu and Toumazet

  • Date: 02/27/2007
Lecturer(s):

Soojin Cho (Ajou University, South Korea)

Location: 

University of British Columbia

Topic: 

Littlewood-Richardson coefficients are structural constants
of the cohomology ring of Grassmannians and the ring of Schur
functions, and they are counted by the number of skew tableaux with
certain properties. In this talk, we introduce well known reductive
formulae for Littlewood-Richardson coefficients and a conjecture by
King, Tollu and Toumazet on the factorization of Littlewood-Richardson
polynomials (coefficients).

First, we give combinatorial proofs for reduction formulae. Then, we
show that reduction formulae are special cases of a conjecture by King,
Tollu and Toumazet on the factorization of Littlewood-Richardson
polynomials (coefficients). Finally, we give a combinatorial proof of
KTT's conjecture for some special cases, which can be realized as
generalized reduction formulae.

This is a joint work with E. Jung and D. Moon.

Other Information: 

Discrete Math Seminar 2007

Sponsor: 

pims