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Joint eigenfunctions of the quantum Toda lattice and the quantum cohomology of the flag varieties

Research Project

Project/Area Number 16540203
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKeio University

Principal Investigator

IKEDA Kaoru  Keio University, Faculty of Economics, Professor, 経済学部, 教授 (40232178)

Project Period (FY) 2004 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2004: ¥600,000 (Direct Cost: ¥600,000)
KeywordsToda lattice / iso level set / quantization / Radon transform / 等位集合 / フーリエ積分 / 旗多様体
Research Abstract

We considered the quantization of the Toda lattice. Let E be 2n dimensional Euclid space. Let $F$ be the space of Fourier integrals with smooth rapidly decreasing functions. We also consider a certain dual space of F, F'. We see that F' has D-module structure. We see that E has foliation by iso level set of Toda lattice. The Fourier integrals are divided into direction of moduli space and that of iso level sets. We call the restriction of the Fourier integrals to the iso level set of Toda lattice as Radon transform. We can define Radon transform of F'. We show that if we restrict the category of the ring of differential, the D-module structure of F' is preserved. As application we show that the integrability of the quantum Toda lattice.

Report

(3 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • Research Products

    (3 results)

All 2004 Other

All Journal Article (3 results)

  • [Journal Article] 量子化戸田格子の幾何学2004

    • Author(s)
      池田 薫
    • Journal Title

      京都大学数理解析研究所講究録 1382

      Pages: 37-58

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The Toda flows preserving small cells of the flag variety G/B and Kazhdan's x_O grading

    • Author(s)
      Kaoru Ikeda
    • Journal Title

      Journal of Geometry and Physics (to appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The Toda flows preserving small cells of the flag variety G/B and Katzdan's x_0 grading

    • Author(s)
      Kaoru Ikeda
    • Journal Title

      Journal of Geometry and Physics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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