Littlewood-Richardson coefficients, the hive model and Horn inequalities
 
 
Description:  Littlewood-Richardson (LR) coefficients arise as integer multiplicities in the decomposition of products of Schur functions. The hive model is introduced as a means of evaluating these coefficients combinatorially. By using edge rather than vertex labelling of LR-hives it is shown that LR-coefficients are non-zero if and only if a set of essential Horn inequalities are satisfied. It is further shown that the saturation of any one such inequality leads to a factorisation of the corresponding LR-coefficients.
Stretched LR-coefficients are defined by scaling all parts of the partitions labelling the three relevant Schur functions. It is known that stretched LR-coefficients are polynomial in the stretching parameter. If time permits some properties and open problems regarding the nature of these polynomials will be discussed.
Area(s):
Date:  2008-09-19
Start Time:   15:15
Speaker:  Ron King (University of Southampton)
Place:  5.5
Research Groups: -Algebra and Combinatorics
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