The alternating dual Pieri rule and k-branching conjectures for closed k-Schur Katalan functions are proven for strictly decreasing partitions, and the Pieri rule also for all partitions with k large.
Broer, Normality of some nilpotent varieties and coho mology of line bundles on the cotangent bundle of the flag variety, Lie theory and geometry, Progr
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Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions
The alternating dual Pieri rule and k-branching conjectures for closed k-Schur Katalan functions are proven for strictly decreasing partitions, and the Pieri rule also for all partitions with k large.