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Journal Articles Combinatorial Theory Year : 2022

Generalised Howe duality and injectivity of induction: the symplectic case

Thomas Gerber
Jérémie Guilhot
Cédric Lecouvey

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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Dates and versions

hal-03370492 , version 1 (08-10-2021)

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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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