A note on the Howe Duality conjecture for symplectic-orthogonal and unitary pairs

2025/02/17 by Droschl, Johannes · 1 citation
#22E46 #22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.11551

Abstract

In this short note we expand on recent results on the degenerate principle series I(s,χ) of classical groups associated to s∈ ℂ and a quadratic character χ. In particular, we strengthen the result for s∈ ℝ_{≥ 0}, which allows us to give as a corollary a new proof of the Howe duality conjecture for symplectic-orthogonal and unitary pairs.

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• The spectrum of the symplectic Grassmannian and Mat_n,m

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