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The Sakellaridis-Venkatesh Conjecture for $ U(2)\backslash SO_{2,3}$

Xiaolei Wan

Abstract

This article gives the Plancherel decomposition of $L^2\left(U(2)(F)\backslash SO_{2,3}(F)\right)$, where $F$ is a local field with characteristic $0$, and the relative character identities. Finally, we obtain a factorization of the global period $P_{U(2)}$.

The Sakellaridis-Venkatesh Conjecture for $ U(2)\backslash SO_{2,3}$

Abstract

This article gives the Plancherel decomposition of , where is a local field with characteristic , and the relative character identities. Finally, we obtain a factorization of the global period .

Paper Structure

This paper contains 40 sections, 61 theorems, 391 equations.

Table of Contents

  1. Introduction
  2. Strongly tempered varieties
  3. Whittaker varieties
  4. Bernstein's method
  5. Relative character
  6. Plancherel decompositions
  7. Whittaker-torus periods
  8. Weil representation
  9. Weil representation
  10. Spherical function
  11. Weil representation for $PGO(V)\times PGSp(W)$
  12. Smooth Weil representation for $PGO(V)\times PGSp(W)$
  13. The actions
  14. $L^2$-Weil representation for $PGO(V)\times PGSp(W)$
  15. The map $A_{\sigma}$
  16. ...and 25 more sections

Key Result

Lemma 1

Theorems & Definitions (102)

  • Definition 1
  • Definition 2
  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • proof
  • ...and 92 more