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2005 Fiscal Year Final Research Report Summary

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
KeywordsToda lattice / iso level set / quantization / Radon transform
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.

  • Research Products

    (2 results)

All Other

All Journal Article (2 results)

  • [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
  • [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

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Published: 2007-12-13  

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