Vanishing of one-dimensional L2-cohomologies of loop groups

Shigeki Aida

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Let G be a simply connected compact Lie group. Let Le(G) be the based loop group with the base point e which is the identity element. Let νe be the pinned Brownian motion measure on Le(G) and let α∈L2({caret insertion point}1T*Le(G),νe)∩D,p({caret insertion point}1T*Le(G),νe) (1<p<2) be a closed 1-form on Le(G). Using results in rough path analysis, we prove that there exists a measurable function f on Le(G) such that df=α. Moreover we prove that dimker =0 for the Hodge-Kodaira type operator acting on 1-forms on Le(G).

Original languageEnglish
Pages (from-to)2164-2213
Number of pages50
JournalJournal of Functional Analysis
Volume261
Issue number8
DOIs
Publication statusPublished - 2011 Oct 15

Keywords

  • Hodge-Kodaira theorem
  • L2-cohomology
  • Loop group
  • Rough path analysis
  • Vanishing theorem

ASJC Scopus subject areas

  • Analysis

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