The odd LittlewoodRichardson rule
In previous work with Mikhail Khovanov and Aaron Lauda we introduced two odd analogues of the Schur functions: one via the combinatorics of Young tableaux (odd Kostka numbers) and one via an odd symmetrization operator. In this paper we introduce a third analogue, the plactic Schur functions. We show they coincide with both previously defined types of Schur function, confirming a conjecture. Using the plactic definition, we establish an odd LittlewoodRichardson rule. We also re-cast this rule in the language of polytopes, via the KnutsonTao hive model.
littlewoodrichardson hives symmetric functions hopf algebras supalgebra odd symmetric functions schubert calculus