Growth Diagrams and Non-symmetric Cauchy Identities on NW (SE) Near Staircases

Azenhas, Olga; Emami, Aram

doi:10.1007/978-3-319-16118-1_4

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The Bijection1

A Combinatorial Cauchy Kernel Expansion Over Near Staircases1

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2024

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Cited by 2 publications

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“…For k > 0, we use Theorem 1, (c), to prove (a) ⇔ (b). The detailed proof can be found in Azenhas and Emami (2014). Once we have proved this, (a) ⇔ (c) follows now from Theorem 1, (d).…”

Section: The Bijectionmentioning

confidence: 62%

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NW-SE expansions of non-symmetric Cauchy kernels on near staircases and growth diagrams

Azenhas,

Emami

2014

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Lascoux has given a triangular version of the Cauchy identity where Schur polynomials are replaced by Demazure characters and Demazure atoms. He has then used the staircase expansion to recover expansions for all Ferrers shapes, where the Demazure characters and Demazure atoms are under the action of Demazure operators specified by the cells above the staircase. The characterisation of the tableau-pairs in these last expansions is less explicit. We give here a bijective proof for expansions over near staircases, where the tableau-pairs are made explicit. Our analysis formulates Mason's RSK analogue, for semi-skylines augmented fillings, in terms of growth diagrams.

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“…For k > 0, we use Theorem 1, (c), to prove (a) ⇔ (b). The detailed proof can be found in Azenhas and Emami (2014). Once we have proved this, (a) ⇔ (c) follows now from Theorem 1, (d).…”

Section: The Bijectionmentioning

confidence: 62%

“…The proof is by double induction on p ≥ 0 and k − p ≥ 0. For p ≥ 0 and k − p= 0, and vice-versa, see Azenhas and Emami (2014). Let p, k − p ≥ 1.…”

Section: A Combinatorial Cauchy Kernel Expansion Over Near Staircasesmentioning

confidence: 99%