• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Computation of boundary components of fundamental domains of symmetric cones and its application

Research Project

Project/Area Number 26400004
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionYamagata University

Principal Investigator

Hayata Takahiro  山形大学, 大学院理工学研究科, 准教授 (50312757)

Research Collaborator ODA Takayuki  沖縄科学技術大学院大学, 教授 (10109415)
WATANABE Takao  大阪大学, 理学研究科, 教授 (30201198)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsエルミート定数 / 基本領域 / ジーゲル上半空間 / 最小ベクトル / キス数 / 球充填問題 / 格子 / シンプレクティック格子 / ランキン定数 / 完全行列 / シンプレクティック群
Outline of Final Research Achievements

In this research, we propose an algorithm computing the kissing number of an element of classical groups and apply them to concrete cases. This algorithm uses the evaluation of determinants of the positive definite symmetric matrices in the Minkowski domain and so-called the short vector algorithm. The height of the linear transformation is by definition the modified ratio of the covolume of the transformed sublattice in the isotropic space and the covolume of the whole fixed lattice. The density is the minimum value of the height among modular transformation of the lattice and the kissing number is its cardinality modulo certain modular transformations. These are a generalization of the classical sphere packing problem. An application is when the symplectic group of degree 2, matrix size 4 and when the totally isotropic space is chosen. In this case, there
are three kinds of symplectic lattices who have locally maximal kissing numbers.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (3 results)

All 2016 2015

All Presentation (3 results) (of which Invited: 1 results)

  • [Presentation] Short vector algorithm and the kissing number on the Siegel-Gottschling fundamental domain of degree 22016

    • Author(s)
      早田 孝博
    • Organizer
      ミニワークショップModular forms and period integrals
    • Place of Presentation
      東京大学駒場キャンパス
    • Related Report
      2016 Annual Research Report
  • [Presentation] Computing Kissing Numbers on Classical Groups2016

    • Author(s)
      早田 孝博
    • Organizer
      金沢数論ミニ集会2016
    • Place of Presentation
      金沢大学サテライトプラザ
    • Related Report
      2016 Annual Research Report
  • [Presentation] 0 cells of the Siegel-Gottschling fundamental domain of degree 22015

    • Author(s)
      Takahiro HAYATA
    • Organizer
      MCM2015Autumn
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2015-10-29
    • Related Report
      2015 Research-status Report
    • Invited

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi