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Generalised Howe duality and injectivity of induction: the symplectic case

Abstract : We study the symplectic Howe duality using two new and independent combinatorial methods: via determinantal formulae on the one hand, and via (bi)crystals on the other hand. The first approach allows us to establish a generalised version where weight multiplicities are replaced by branching coefficients. In turn, this generalised Howe duality is used to prove the injectivity of induction for Levi branchings as previously conjectured by the last two authors.
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https://hal.archives-ouvertes.fr/hal-03370492
Contributor : Cédric Lecouvey Connect in order to contact the contributor
Submitted on : Friday, October 8, 2021 - 9:12:59 AM
Last modification on : Saturday, December 3, 2022 - 8:42:35 AM
Long-term archiving on: : Sunday, January 9, 2022 - 6:20:29 PM

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Thomas Gerber, Jérémie Guilhot, Cédric Lecouvey. Generalised Howe duality and injectivity of induction: the symplectic case. Combinatorial Theory, 2022, 2 (2), ⟨10.5070/C62257878⟩. ⟨hal-03370492⟩

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