Defining relations of fusion products and Schur positivity

Abstract

In this note we give defining relations of an ${\mathfrak{sl}}_{n+1}[t]$-module defined by the fusion product of simple ${\mathfrak{sl}}_{n+1}$-modules whose highest weights are multiples of a given fundamental weight. From this result we obtain a surjective homomorphism between two fusion products, which can be considered as a current algebra analog of Schur positivity.

13 pages; added references

References in corpus (1)

• A Steinberg type decomposition theorem for higher level Demazure modules

Cited by in corpus (1)

• Graded limits of simple tensor product of Kirillov-Reshetikhin modules for $U_q({\widetilde{\mathfrak{sl}}}_{n+1})$