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Cartan coherent configurations. / Ponomarenko, Ilia; Vasil’ev, Andrey.

In: Journal of Algebraic Combinatorics, Vol. 45, No. 2, 01.03.2017, p. 525-552.

Research output: Contribution to journal › Article › peer-review

Harvard

Ponomarenko, I & Vasil’ev, A 2017, 'Cartan coherent configurations', Journal of Algebraic Combinatorics, vol. 45, no. 2, pp. 525-552. https://doi.org/10.1007/s10801-016-0715-5

APA

Ponomarenko, I., & Vasil’ev, A. (2017). Cartan coherent configurations. Journal of Algebraic Combinatorics, 45(2), 525-552. https://doi.org/10.1007/s10801-016-0715-5

Vancouver

Ponomarenko I, Vasil’ev A. Cartan coherent configurations. Journal of Algebraic Combinatorics. 2017 Mar 1;45(2):525-552. doi: 10.1007/s10801-016-0715-5

Author

Ponomarenko, Ilia ; Vasil’ev, Andrey. / Cartan coherent configurations. In: Journal of Algebraic Combinatorics. 2017 ; Vol. 45, No. 2. pp. 525-552.

BibTeX

@article{9f7821ef628d4d8a93b6a3e79eb9ce7a,
title = "Cartan coherent configurations",
abstract = "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.",
author = "Ilia Ponomarenko and Andrey Vasil{\textquoteright}ev",
note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",
year = "2017",
month = mar,
day = "1",
doi = "10.1007/s10801-016-0715-5",
language = "English",
volume = "45",
pages = "525--552",
journal = "Journal of Algebraic Combinatorics",
issn = "0925-9899",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - Cartan coherent configurations

AU - Ponomarenko, Ilia

AU - Vasil’ev, Andrey

N1 - Publisher Copyright: © 2016, Springer Science+Business Media New York.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84991309773&partnerID=8YFLogxK

U2 - 10.1007/s10801-016-0715-5

DO - 10.1007/s10801-016-0715-5

M3 - Article

AN - SCOPUS:84991309773

VL - 45

SP - 525

EP - 552

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

SN - 0925-9899

IS - 2

ER -

ID: 10321327