Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 058, 9 pages      arXiv:1403.4750
Contribution to the Special Issue on New Directions in Lie Theory

Schur Positivity and Kirillov-Reshetikhin Modules

Ghislain Fourier a and David Hernandez b
a) School of Mathematics and Statistics, University of Glasgow, UK
b) Sorbonne Paris Cité, Univ Paris Diderot-Paris 7, Institut de Mathématiques de Jussieu - Paris Rive Gauche CNRS UMR 7586, Bât. Sophie Germain, Case 7012,75205 Paris, France

Received April 04, 2014, in final form May 29, 2014; Published online June 04, 2014

In this note, inspired by the proof of the Kirillov-Reshetikhin conjecture, we consider tensor products of Kirillov-Reshetikhin modules of a fixed node and various level. We fix a positive integer and attach to each of its partitions such a tensor product. We show that there exists an embedding of the tensor products, with respect to the classical structure, along with the reverse dominance relation on the set of partitions.

Key words: Kirillov-Reshetikhin modules; $Q$-systems; Schur positivity.

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