The inverse reduction map in the quantum Littlewood-Richardson bijection

Summary · qwen2.5:32b

The article details a method to decompose a symplectic column into fixed and disjoint parts under parity involution, which uniquely determines the inverse of the reduction map in the quantum Littlewood-Richardson bijection; this decomposition enables explicit construction of the inverse using combinatorial $R$-matrices and shorter reduction maps as outlined by Watanabe.

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Exploring the inverse reduction map in quantum Littlewood-Richardson bijection, a topic in advanced mathematics.

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arXiv:2606.24840v2 Announce Type: replace Abstract: We decompose a symplectic column by detaching its maximal nonempty intervals that are fixed by the parity involution, this is the part of the symplectic column that is fixed by that involution, and the remaining part consisting of the subword whose image under the parity involution is disjoint of the symplectic column. The parity involution swaps an even number with the previous odd number and an odd number with the next even number. That decomposition is uniquely determined by the symplectic column and the symplectic conditions satisfied by those pieces pack the needed information to explicitly write the inverse of the reduction map in the quantum Littlewood-Richardson bijection. The tools provided here can be combined with the composition of the inverses of the several maps in which the reduction map decomposes, given by Watanabe, namely, among them, combinatorial $R$-matrices and reduction maps on shorter symplectic columns.