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March 29, 2026Journal of Lie theory0 citationsOpen Access

Sur la Conjecture de Corwin-Greenleaf

HFH. Fujiwara

Key Points

  • The study aims to prove the Corwin-Greenleaf conjecture related to representations in nilpotent Lie groups.
  • Defined the nilpotent Lie group G and closed subgroup H.
  • Analyzed the unitary character of H and its induced representation on G.
  • Explored the condition of finite multiplicities of irreducible representations.
  • Investigated the algebraic structure of differential operators that commute with induced representations.
  • Demonstrated that the algebra of differential operators D(G/H) is isomorphic to C[H], under the condition that H-orbits in G are one-dimensional.

Abstract

Let G=exp( g) be a nilpotent Lie group, H=exp( h) a closed subgroup of G .Let = f be a unitary character of H and = ind G H the induced representation of G .Let us suppose that the multiplicities of the irreducible representations occuring in the disintegration of are finite.We prove in this note the conjecture of Corwin-Greenleaf, which says that the algebra D (G/H) of the differential operators which commute with is isomorhic to the algebra C H under the condition that the H -orbits in are of dimension 1 .

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Cite This Study

H. Fujiwara (1997) studied this question.

synapsesocial.com/papers/69c8c115de0f0f753b39bb97https://doi.org/10.5802/jolt.114
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