The odd Littlewood-Richardson rule

Details The odd Littlewood-Richardson rule The odd Littlewood-Richardson rule

2011-11-16

arxiv.org/abs/1111.3932v1

Mathematics

Quantum Algebra

20 pages, 2 figures

Scientific paper

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 the 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 Littlewood-Richardson rule. We also re-cast this rule in the language of polytopes, via the Knutson-Tao hive model.

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