References
- H. Abe, Young diagrams and intersection numbers for toric manifolds associated with Weyl chambers, Electron. J. Combin. 22 (2015), no. 2, Paper 2.4, 24 pp. https://doi.org/10.37236/4307
- A. Al-Raisi, Equivariance, module structure, branched covers, strickland maps and co-homology related to the polyhedral product functor, Doctoral dissertation, University of Rochester, 2014.
- A. Bahri, M. Bendersky, F. Cohen, and S. Gitler, The polyhedral product functor: a method of decomposition for moment-angle complexes, arrangements and related spaces, Adv. Math. 225 (2010), no. 3, 1634-1668. https://doi.org/10.1016/j.aim.2010.03.026
- M. Benard, On the Schur indices of characters of the exceptional Weyl groups, Ann. of Math. (2) 94 (1971), 89-107. https://doi.org/10.2307/1970736
- A. Bjorner, Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings, Adv. in Math. 52 (1984), no. 3, 173-212. https://doi.org/10.1016/0001-8708(84)90021-5
- L. Cai and S. Choi, On the topology of a small cover associated to a shellable complex, preprint, arXiv:1604.06988, 2016.
- S. Choi, S. Kaji, and H. Park, The cohomology groups of real toric varieties associated to Weyl chambers of type C and D, preprint, arXiv:1705.00275, 2017.
- S. Choi, S. Kaji, and S. Theriault, Homotopy decomposition of a suspended real toric space, Bol. Soc. Mat. Mex. (3) 23 (2017), no. 1, 153-161. https://doi.org/10.1007/s40590-016-0090-1
- S. Choi, B. Park, and H. Park, The Betti numbers of real toric varieties associated to Weyl chambers of type B, Chin. Ann. Math. Ser. B 38 (2017), no. 6, 1213-1222. https://doi.org/10.1007/s11401-017-1032-6
- S. Choi and H. Park, A new graph invariant arises in toric topology, J. Math. Soc. Japan 67 (2015), no. 2, 699-720. https://doi.org/10.2969/jmsj/06720699
- S. Choi and H. Park, On the cohomology and their torsion of real toric objects, Forum Math. 29 (2017), no. 3, 543-553. https://doi.org/10.1515/forum-2016-0025
- CHomP, Computational homology project, http://chomp.rutgers.edu/.
- M. W. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), no. 2, 417-451. https://doi.org/10.1215/S0012-7094-91-06217-4
- I. Dolgachev and V. Lunts, A character formula for the representation of a Weyl group in the cohomology of the associated toric variety, J. Algebra 168 (1994), no. 3, 741-772. https://doi.org/10.1006/jabr.1994.1251
- M. Geck and G. Pfeiffer, Characters of finite Coxeter groups and Iwahori-Hecke algebras, London Mathematical Society Monographs. New Series, 21, The Clarendon Press, Oxford University Press, New York, 2000.
- L. Geissinger and D. Kinch, Representations of the hyperoctahedral groups, J. Algebra 53 (1978), no. 1, 1-20. https://doi.org/10.1016/0021-8693(78)90200-4
- P. Hanlon, The characters of the wreath product group acting on the homology groups of the Dowling lattices, J. Algebra 91 (1984), no. 2, 430-463. https://doi.org/10.1016/0021-8693(84)90113-3
- A. Henderson, Rational cohomology of the real Coxeter toric variety of type A, in Configuration spaces, 313-326, CRM Series, 14, Ed. Norm., Pisa, 2012. https://doi.org/10.1007/978-88-7642-431-1_14
- A. Henderson and G. Lehrer, The equivariant Euler characteristic of real Coxeter toric varieties, Bull. Lond. Math. Soc. 41 (2009), no. 3, 515-523. https://doi.org/10.1112/blms/bdp023
- J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics, 29, Cambridge University Press, Cambridge, 1990. https://doi.org/10.1017/CBO9780511623646
- P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167-189. https://doi.org/10.1007/BF01392549
- C. Procesi, The toric variety associated to Weyl chambers, in Mots, 153-161, Lang. Raison. Calc, Hermes, Paris, 1990.
- E. M. Rains, The homology of real subspace arrangements, J. Topol. 3 (2010), no. 4, 786-818. https://doi.org/10.1112/jtopol/jtq027
- B. E. Sagan, The Symmetric Group, second edition, Graduate Texts in Mathematics, 203, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4757-6804-6
- L. Solomon, A decomposition of the group algebra of a finite Coxeter group, J. Algebra 9 (1968), 220-239. https://doi.org/10.1016/0021-8693(68)90022-7
- R. P. Stanley, Some aspects of groups acting on finite posets, J. Combin. Theory Ser. A 32 (1982), no. 2, 132-161. https://doi.org/10.1016/0097-3165(82)90017-6
- R. P. Stanley, Log-concave and unimodal sequences in algebra, combinatorics, and geometry, in Graph theory and its applications: East and West (Jinan, 1986), 500-535, Ann. New York Acad. Sci., 576, New York Acad. Sci., New York, 1989. https://doi.org/10.1111/j.1749-6632.1989.tb16434.x
- J. R. Stembridge, Some permutation representations of Weyl groups associated with the cohomology of toric varieties, Adv. Math. 106 (1994), no. 2, 244-301. https://doi.org/10.1006/aima.1994.1058
- A. I. Suciu, The rational homology of real toric manifolds, Oberwolfach Reports 2012 (2012), no. 4, 2972-2976.
- S. Sundaram, The homology representations of the symmetric group on Cohen-Macaulay subposets of the partition lattice, Adv. Math. 104 (1994), no. 2, 225-296. https://doi.org/10.1006/aima.1994.1030
- M. L. Wachs, Poset topology: tools and applications, in Geometric combinatorics, 497-615, IAS/Park City Math. Ser., 13, Amer. Math. Soc., Providence, RI, 2007.