Cartan coherent configurations

Ilia Ponomarenko, Andrey Vasil’ev

Результат исследования: Научные публикации в периодических изданияхстатья

2 Цитирования (Scopus)

Аннотация

The Cartan scheme X of a finite group G with a (B, N)-pair is defined to be the coherent configuration associated with the action of G on the right cosets of the Cartan subgroup B∩ N by right multiplication. It is proved that if G is a simple group of Lie type, then asymptotically the coherent configuration X is 2-separable, i.e., the array of 2-dimensional intersection numbers determines X up to isomorphism. It is also proved that in this case, the base number of X equals 2. This enables us to construct a polynomial-time algorithm for recognizing Cartan schemes when the rank of G and the order of the underlying field are sufficiently large. One of the key points in the proof is a new sufficient condition for an arbitrary homogeneous coherent configuration to be 2-separable.

Язык оригиналаанглийский
Страницы (с-по)525-552
Число страниц28
ЖурналJournal of Algebraic Combinatorics
Том45
Номер выпуска2
DOI
СостояниеОпубликовано - 1 мар 2017

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