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For a G-manifold X with a proper and transitive action by a reductive subgroup L, there exists a natural L-equivariant fiber bundle structure of X over the Riemannian symmetric space associated with L, with a compact fiber F. This chapter explores three key topics: Furthermore, there are three natural rings of differential operators on X: The rings (a) and (b) underlie (1) and (2), respectively. If L additionally acts spherically on X, the elements in these three rings (a), (b), and (c) are commutative, and (c) becomes an underlying structure of (3). Building on this, we introduce transfer maps to establish a connection between (1) and (2) via the well-understood harmonic analysis on the compact fiber. The results presented in this chapter play a key role in proving our main results.

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Differential Operators Coming from L and from the Fiber F

  • 章节

  • 发表日期：

    2025年

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  • Fanny Kassel,
  • Toshiyuki Kobayashi

摘要

For a G-manifold X with a proper and transitive action by a reductive subgroup L, there exists a natural L-equivariant fiber bundle structure of X over the Riemannian symmetric space associated with L, with a compact fiber F. This chapter explores three key topics: Furthermore, there are three natural rings of differential operators on X: The rings (a) and (b) underlie (1) and (2), respectively. If L additionally acts spherically on X, the elements in these three rings (a), (b), and (c) are commutative, and (c) becomes an underlying structure of (3). Building on this, we introduce transfer maps to establish a connection between (1) and (2) via the well-understood harmonic analysis on the compact fiber. The results presented in this chapter play a key role in proving our main results.