Connection between the Plancherel formula and the Howe dual pair (Sp(2n, ℝ), O(k))

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Abstract

Let D be the bounded symmetric domain {w ∈ Sym(2n, ℂ)| I2n - ww̄ ≫ 0}. In this article, we describe explicitly the Plancherel formula of a weighted Bergman space on D under the action of Spc(2n, ℝ) × Spc(2n, ℝ) by using the Howe dual pair (Spc(2n, ℝ), O(k)).

Original languageEnglish
Pages (from-to)743-760
Number of pages18
JournalMathematische Zeitschrift
Volume241
Issue number4
DOIs
Publication statusPublished - Dec 2002
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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