The Regularized Siegel-Weil Formula (The Second Term Identity) and the Rallis Inner Product Formula
Wee Teck Gan, Yannan Qiu, Shuichiro Takeda
TL;DR
This paper proves the second term identity of the Siegel-Weil formula and derives the Rallis inner product formula for global theta lifts, resolving key non-vanishing issues in automorphic representation theory.
Contribution
It establishes the second term identity of the Siegel-Weil formula in full generality and derives the Rallis inner product formula for all dual pairs.
Findings
Proved the second term identity of the Siegel-Weil formula.
Derived the Rallis inner product formula for global theta lifts.
Resolved the non-vanishing problem of global theta lifts.
Abstract
In this paper, we establish the second term identity of the Siegel-Weil formula in full generality, and derive the Rallis inner product formula for global theta lifts for any dual pair. As a corollary, we resolve the non-vanishing problem of global theta lifts initiated by Steve Rallis.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics