Configurations of seven lines on the real projective plane and the root system of type E_7

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Let l<SUB>1</SUB>, l<SUB>2</SUB>, •s, l<SUB>7</SUB> be mutually different seven lines on the real projective plane. We consider two conditions; (A) No three of l<SUB>1</SUB>, l<SUB>2</SUB>, •s, l<SUB>7</SUB> intersect at a point. (B) There is no conic tangent to any six of l<SUB>1</SUB>, l<SUB>2</SUB>, •s, l<SUB>7</SUB>. Cummings [{3}] and White [{16}] showed that there are eleven non-equivalent classes of systems of seven lines with condition (A) (cf. [{7}], Chap. 18). The purposes of this article is to give an interpretation of the classification of Cummings and White in terms of the root system of type E<SUB>7</SUB>. To accomplish this, it is better to add condition (B) for systems of seven lines. Moreover we need the notion of tetrahedral sets which consist of ten roots modulo signs in the root system of type E<SUB>7</SUB> and which plays an important role in our study.

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  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 51(4), 987-1013, 1999-10-01 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10004480996
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    4895030
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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