Parabolic subgroup of a reflection group (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Parabolic subgroup of a reflection group" in English language version.

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34doi.org

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27semanticscholar.org

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8arxiv.org

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1emis.de

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1harvard.edu

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arxiv.org

Nuida (2012). Nuida, Koji (2012), "Locally parabolic subgroups in Coxeter groups of arbitrary ranks", Journal of Algebra, 350: 207–217, arXiv:1006.4709, doi:10.1016/j.jalgebra.2011.11.005
Reiner, Ripoll & Stump (2017), Example 1.2. Reiner, Victor; Ripoll, Vivien; Stump, Christian (2017), "On non-conjugate Coxeter elements in well-generated reflection groups", Mathematische Zeitschrift, 285 (3–4): 1041–1062, arXiv:1404.5522, doi:10.1007/s00209-016-1736-4, S2CID 253752187
Baumeister et al. (2017), Proposition 1.4 and Corollary 4.4. Baumeister, Barbara; Gobet, Thomas; Roberts, Kieran; Wegener, Patrick (2017), "On the Hurwitz action in finite Coxeter groups", Journal of Group Theory, 20 (1): 103–131, arXiv:1512.04764, doi:10.1515/jgth-2016-0025, S2CID 44035800
Gobet (2017), Example 2.2. Gobet, Thomas (2017), "On cycle decompositions in Coxeter groups", Séminaire Lotharingien de Combinatoire, 78B: Art. 45, arXiv:1611.03442
Taylor (2012). Taylor, D.E. (2012), "Reflection subgroups of finite complex reflection groups", Journal of Algebra, 366: 218–234, arXiv:1201.1348, doi:10.1016/j.jalgebra.2012.04.033
McCammond & Sulway (2017). McCammond, Jon; Sulway, Robert (2017), "Artin groups of Euclidean type", Inventiones Mathematicae, 210 (1): 231–282, arXiv:1312.7770, Bibcode:2017InMat.210..231M, doi:10.1007/s00222-017-0728-2, S2CID 253738806
Cumplido et al. (2019). Cumplido, María; Gebhardt, Volker; González-Meneses, Juan; Wiest, Bert (2019), "On parabolic subgroups of Artin–Tits groups of spherical type", Advances in Mathematics, 352: 572–610, arXiv:1712.06727, doi:10.1016/j.aim.2019.06.010
González-Meneses & Marin (2022). González-Meneses, Juan; Marin, Ivan (2022), Parabolic subgroups of complex braid groups I, arXiv:2208.11938v1

doi.org

Kane (2001), p. 1. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Kane (2001), pp. 8–14. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Humphreys (1990), pp. xi–xii. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), §1.9. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Kane (2001), p. 160. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Humphreys (1990), p. 66. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Björner & Brenti (2005), §2.4. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Humphreys (1990), §5.5. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), §1.10. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), §5.10. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Björner & Brenti (2005), p. 17. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Humphreys (1990), §5.12. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Björner & Brenti (2005), p. 41. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Björner & Brenti (2005), pp. 86–7. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Björner & Brenti (2005), p. 39. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Humphreys (1990), pp. 118, 129. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Kane (2001), p. 60. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Orlik & Terao (1992), p. 215. Orlik, Peter; Terao, Hiroaki (1992), Arrangements of Hyperplanes, Grundlehren der mathematischen Wissenschaften, Springer, doi:10.1007/978-3-662-02772-1, ISBN 978-3-540-55259-8
Orlik & Terao (1992), §2.1. Orlik, Peter; Terao, Hiroaki (1992), Arrangements of Hyperplanes, Grundlehren der mathematischen Wissenschaften, Springer, doi:10.1007/978-3-662-02772-1, ISBN 978-3-540-55259-8
Broué (2010), §4.2.4. Broué, Michel (2010), Introduction to Complex Reflection Groups and Their Braid Groups, Lecture Notes in Mathematics, vol. 1988, Springer-Verlag, doi:10.1007/978-3-642-11175-4, ISBN 978-3-642-11174-7
Kane (2001), §5.2. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Kane (2001), p. 58. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Björner & Brenti (2005), p. 248. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Nuida (2012). Nuida, Koji (2012), "Locally parabolic subgroups in Coxeter groups of arbitrary ranks", Journal of Algebra, 350: 207–217, arXiv:1006.4709, doi:10.1016/j.jalgebra.2011.11.005
Reiner, Ripoll & Stump (2017), Example 1.2. Reiner, Victor; Ripoll, Vivien; Stump, Christian (2017), "On non-conjugate Coxeter elements in well-generated reflection groups", Mathematische Zeitschrift, 285 (3–4): 1041–1062, arXiv:1404.5522, doi:10.1007/s00209-016-1736-4, S2CID 253752187
Baumeister et al. (2017), Proposition 1.4 and Corollary 4.4. Baumeister, Barbara; Gobet, Thomas; Roberts, Kieran; Wegener, Patrick (2017), "On the Hurwitz action in finite Coxeter groups", Journal of Group Theory, 20 (1): 103–131, arXiv:1512.04764, doi:10.1515/jgth-2016-0025, S2CID 44035800
Humphreys (1990), p. 114. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), p. 96. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Kane (2001), p. 130. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Humphreys (1990), p. 136. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Taylor (2012). Taylor, D.E. (2012), "Reflection subgroups of finite complex reflection groups", Journal of Algebra, 366: 218–234, arXiv:1201.1348, doi:10.1016/j.jalgebra.2012.04.033
McCammond & Sulway (2017). McCammond, Jon; Sulway, Robert (2017), "Artin groups of Euclidean type", Inventiones Mathematicae, 210 (1): 231–282, arXiv:1312.7770, Bibcode:2017InMat.210..231M, doi:10.1007/s00222-017-0728-2, S2CID 253738806
Cumplido et al. (2019). Cumplido, María; Gebhardt, Volker; González-Meneses, Juan; Wiest, Bert (2019), "On parabolic subgroups of Artin–Tits groups of spherical type", Advances in Mathematics, 352: 572–610, arXiv:1712.06727, doi:10.1016/j.aim.2019.06.010
Broué (2010), §4.2.5. Broué, Michel (2010), Introduction to Complex Reflection Groups and Their Braid Groups, Lecture Notes in Mathematics, vol. 1988, Springer-Verlag, doi:10.1007/978-3-642-11175-4, ISBN 978-3-642-11174-7

emis.de

Gobet (2017), Example 2.2. Gobet, Thomas (2017), "On cycle decompositions in Coxeter groups", Séminaire Lotharingien de Combinatoire, 78B: Art. 45, arXiv:1611.03442

harvard.edu

ui.adsabs.harvard.edu

McCammond & Sulway (2017). McCammond, Jon; Sulway, Robert (2017), "Artin groups of Euclidean type", Inventiones Mathematicae, 210 (1): 231–282, arXiv:1312.7770, Bibcode:2017InMat.210..231M, doi:10.1007/s00222-017-0728-2, S2CID 253738806

semanticscholar.org

api.semanticscholar.org

Kane (2001), p. 1. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Kane (2001), pp. 8–14. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Humphreys (1990), pp. xi–xii. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), §1.9. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Kane (2001), p. 160. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Humphreys (1990), p. 66. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Björner & Brenti (2005), §2.4. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Humphreys (1990), §5.5. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), §1.10. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), §5.10. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Björner & Brenti (2005), p. 17. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Humphreys (1990), §5.12. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Björner & Brenti (2005), p. 41. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Björner & Brenti (2005), pp. 86–7. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Björner & Brenti (2005), p. 39. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Humphreys (1990), pp. 118, 129. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Kane (2001), p. 60. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Kane (2001), §5.2. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Kane (2001), p. 58. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Björner & Brenti (2005), p. 248. Björner, Anders; Brenti, Francesco (2005), Combinatorics of Coxeter groups, Springer, doi:10.1007/3-540-27596-7, ISBN 978-3540-442387, S2CID 115235335
Reiner, Ripoll & Stump (2017), Example 1.2. Reiner, Victor; Ripoll, Vivien; Stump, Christian (2017), "On non-conjugate Coxeter elements in well-generated reflection groups", Mathematische Zeitschrift, 285 (3–4): 1041–1062, arXiv:1404.5522, doi:10.1007/s00209-016-1736-4, S2CID 253752187
Baumeister et al. (2017), Proposition 1.4 and Corollary 4.4. Baumeister, Barbara; Gobet, Thomas; Roberts, Kieran; Wegener, Patrick (2017), "On the Hurwitz action in finite Coxeter groups", Journal of Group Theory, 20 (1): 103–131, arXiv:1512.04764, doi:10.1515/jgth-2016-0025, S2CID 44035800
Humphreys (1990), p. 114. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Humphreys (1990), p. 96. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
Kane (2001), p. 130. Kane, Richard (2001), Reflection groups and invariant theory, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer-Verlag, doi:10.1007/978-1-4757-3542-0, ISBN 0-387-98979-X, S2CID 119694827
Humphreys (1990), p. 136. Humphreys, James E. (1990), Reflection groups and Coxeter groups, Cambridge University Press, doi:10.1017/CBO9780511623646, ISBN 0-521-37510-X, S2CID 121077209
McCammond & Sulway (2017). McCammond, Jon; Sulway, Robert (2017), "Artin groups of Euclidean type", Inventiones Mathematicae, 210 (1): 231–282, arXiv:1312.7770, Bibcode:2017InMat.210..231M, doi:10.1007/s00222-017-0728-2, S2CID 253738806