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Original Articles

Extended symmetric spaces and θ-twisted involution graphs

, , , , , & show all
Pages 2293-2306 | Received 27 Sep 2019, Accepted 23 Nov 2019, Published online: 03 Feb 2020

References

  • Brion, M., Helminck, A. G. (2000). On orbit closures of symmetric subgroups in flag varieties. Can. J. Math. 52(2):265–292. DOI: 10.4153/CJM-2000-012-9.
  • Godsil, C., Royle, G. F. (2013). Algebraic Graph Theory, vol. 207. Berlin, Germany: Springer Science & Business Media.
  • Haas, R., Helminck, A. (2012). Algorithms for twisted involutions in weyl groups. Algebra Colloq. 19(02):263–282. DOI: 10.1142/S100538671200017X.
  • Haas, R., Helminck, A. G. (2011). Admissible sequences for twisted involutions in weyl groups. Can. Math. Bull. 54(4):663–675. DOI: 10.4153/CMB-2011-075-1.
  • Helminck, A. (1989). On the orbits of symmetric spaces under the action of parabolic subgroups. Contemporary Math. 88:435–447.
  • Helminck, A. (1991). Tori invariant under an involutorial automorphism, i. Adv. Math. 85(1):1–38. DOI: 10.1016/0001-8708(91)90048-C.
  • Helminck, A. (1997). Tori invariant under an involutorial automorphism ii. Adv. Math. 131(1):1–92. DOI: 10.1006/aima.1997.1633.
  • Helminck, A. (2000). On the classification of k-involutions. Adv. Math. 153(1):1–117. DOI: 10.1006/aima.1998.1884.
  • Helminck, A., Helminck, G. (1998). A class of parabolic -subgroups associated with symmetric -varieties. Trans. Amer. Math. Soc. 350(11):4669–4691. DOI: 10.1090/S0002-9947-98-02029-7.
  • Helminck, A., Hilgert, J., Neumann, A., Ólafsson, G. (1999). A conjugacy theorem for symmetric spaces. Math. Ann. 313(4):785–791. DOI: 10.1007/s002080050282.
  • Helminck, A. G. (1988). Algebraic groups with a commuting pair of involutions and semisimple symmetric spaces. Adv. Math. 71(1):21–91. DOI: 10.1016/0001-8708(88)90066-7.
  • Helminck, A. G. (1996). Computing b-orbits on g/h. J. Symb. Comput. 21(2):169–209. DOI: 10.1006/jsco.1996.0008.
  • Helminck, A. G. (2000). Computing orbits of minimal parabolic k-subgroups acting on symmetric k-varieties. J. Symb. Comput. 30(5):521–553. DOI: 10.1006/jsco.2000.0395.
  • Helminck, A. G. (2004). Combinatorics related to orbit closures of symmetric subgroups in flag varieties. In: Invariant Theory in All Characteristics, CRM Proc. Lecture Notes. Vol. 35. Providence, Rhode Island: American Mathematical Society, pp. 71–90.
  • Helminck, A. G., Helminck, G. F. (2002). Spherical distribution vectors. Acta Appl. Math. 73(1/2):39–57. DOI: 10.1023/A:1019762302447.
  • Helminck, A. G., Helminck, G. F. (2005). Multiplicity one for representations corresponding to spherical distribution vectors of class ρ. Acta Appl. Math. 86(1-2):21–48. DOI: 10.1007/s10440-005-0461-5.
  • Helminck, A. G., Schwarz, G. W. (2004). Smoothness of quotients associated with a pair of commuting involutions. Can. J. Math. 56(5):945–962. DOI: 10.4153/CJM-2004-043-7.
  • Helminck, A. G., Schwarz, G. W. (2009). Real double coset spaces and their invariants. J. Algebra 322(1):219–236. DOI: 10.1016/j.jalgebra.2009.01.028.
  • Helminck, A. G., Schwarz, G. W. (2011). On generalized cartan subspaces. Transform. Groups. 16(3):783–805. DOI: 10.1007/s00031-011-9151-8.
  • Helminck, A. G., Schwarz, G. W. (2001). Orbits and invariants associated with a pair of commuting involutions. Duke Math. J. 106(2):237–279. DOI: 10.1215/S0012-7094-01-10622-4.
  • Helminck, A. G., Wang, S. P. (1993). On rationality properties of involutions of reductive groups. Adv. Math. 99(1):26–96. DOI: 10.1006/aima.1993.1019.
  • Richardson, R., Springer, T. A. (1990). The bruhat order on symmetric varieties. Geom. Dedicata 35(1-3):389–436. DOI: 10.1007/BF00147354.
  • Winebarger, J. T. Poset Diagrams for Twisted Involutions of Weyl Groups (2014). Honor's thesis. Appalachian State University.

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