{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T08:09:51Z","timestamp":1744186191285},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2010,2,6]],"date-time":"2010-02-06T00:00:00Z","timestamp":1265414400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2010,6]]},"DOI":"10.1007\/s10208-010-9058-0","type":"journal-article","created":{"date-parts":[[2010,2,5]],"date-time":"2010-02-05T19:06:59Z","timestamp":1265396819000},"page":"245-274","source":"Crossref","is-referenced-by-count":10,"title":["The Chow Rings of Generalized Grassmannians"],"prefix":"10.1007","volume":"10","author":[{"given":"Haibao","family":"Duan","sequence":"first","affiliation":[]},{"given":"Xuezhi","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,2,6]]},"reference":[{"key":"9058_CR1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/0040-9383(86)90012-1","volume":"7","author":"P. Baum","year":"1968","unstructured":"P. Baum, On the cohomology of homogeneous spaces, Topology 7, 15\u201338 (1968).","journal-title":"Topology"},{"key":"9058_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1070\/RM1973v028n03ABEH001557","volume":"28","author":"I.N. Bernstein","year":"1973","unstructured":"I.N. Bernstein, I.M. Gelfand, S.I. Gelfand, Schubert cells and cohomology of the spaces\u00a0G\/P, Russ. Math. Surv. 28, 1\u201326 (1973).","journal-title":"Russ. Math. Surv."},{"key":"9058_CR3","doi-asserted-by":"crossref","first-page":"115","DOI":"10.2307\/1969728","volume":"57","author":"A. Borel","year":"1953","unstructured":"A. Borel, Sur la\u00a0cohomologie des espaces fibr\u00e9s principaux et des espaces homogenes de\u00a0groupes de\u00a0Lie compacts, Ann. Math. 57, 115\u2013207 (1953).","journal-title":"Ann. Math."},{"key":"9058_CR4","doi-asserted-by":"crossref","first-page":"458","DOI":"10.2307\/2372795","volume":"80","author":"A. Borel","year":"1958","unstructured":"A. Borel, F. Hirzebruch, Characteristic classes and homogeneous spaces\u00a0(I), Am. J. Math. 80, 458\u2013538 (1958).","journal-title":"Am. J. Math."},{"key":"9058_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3951-0","volume-title":"Differential Forms in Algebraic Topology, Graduate Texts in Mathematics","author":"R. Bott","year":"1982","unstructured":"R. Bott, L. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics, vol.\u00a082 (Springer, New York\/Berlin, 1982)."},{"key":"9058_CR6","series-title":"Proceedings of Symposia in Pure Mathematics","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/pspum\/056.1\/1278698","volume-title":"Algebraic Groups and Their Generalizations: Classical Methods","author":"C. Chevalley","year":"1994","unstructured":"C. Chevalley, Sur les d\u00e9compositions cellulaires des espaces\u00a0G\/B, in Algebraic Groups and Their Generalizations: Classical Methods, ed. by W. Haboush, B. Parshall, Proceedings of Symposia in Pure Mathematics, vol.\u00a056 (part\u00a01) (AMS, Providence, 1994), pp.\u00a01\u201326."},{"key":"9058_CR7","first-page":"575","volume":"16","author":"L. Conlon","year":"1965","unstructured":"L. Conlon, On the topology of EIII and EIV, Proc. Am. Math. Soc. 16, 575\u2013581 (1965).","journal-title":"Proc. Am. Math. Soc."},{"key":"9058_CR8","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/BF01418790","volume":"21","author":"M. Demazure","year":"1973","unstructured":"M. Demazure, Invariants sym\u00e9triques entiers des groupes de\u00a0Weyl et torsion, Invent. Math. 21, 287\u2013301 (1973).","journal-title":"Invent. Math."},{"key":"9058_CR9","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1090\/S0002-9939-00-05734-8","volume":"128","author":"H. Duan","year":"2000","unstructured":"H. Duan, Characteristic classes for complex bundles whose real reductions are trivial, Proc. Am. Math. Soc. 128, 2465\u20132471 (2000).","journal-title":"Proc. Am. Math. Soc."},{"key":"9058_CR10","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s00222-004-0394-z","volume":"159","author":"H. Duan","year":"2005","unstructured":"H. Duan, Multiplicative rule of Schubert classes, Invent. Math. 159, 407\u2013436 (2005).","journal-title":"Invent. Math."},{"key":"9058_CR11","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1142\/S021819670600344X","volume":"16","author":"H. Duan","year":"2006","unstructured":"H. Duan, X. Zhao, Algorithm for multiplying Schubert classes, Int. J. Algebra Comput. 16, 1197\u20131210 (2006).","journal-title":"Int. J. Algebra Comput."},{"issue":"3","key":"9058_CR12","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1007\/s00222-006-0016-z","volume":"177","author":"H. Duan","year":"2009","unstructured":"H. Duan, X. Zhao, Erratum: Multiplicative rule of Schubert classes, Invent. Math. 177(3), 683\u2013684 (2009).","journal-title":"Invent. Math."},{"key":"9058_CR13","unstructured":"H. Duan, X. Zhao, Appendix to \u201cThe Chow rings of generalized Grassmannians\u201d, arXiv:math.AG\/0510085 ."},{"key":"9058_CR14","unstructured":"H. Duan, X. Zhao, The integral cohomology of complete flag manifolds, arXiv:math.AT\/0801.2444 ."},{"key":"9058_CR15","unstructured":"H. Duan, X. Zhao, The cohomology of Lie groups, arXiv:math.AT\/0711.2541 ."},{"key":"9058_CR16","unstructured":"H. Duan, X. Zhao, The Chow rings of generalized Grassmannians, arXiv:math.AG\/0511332 ."},{"key":"9058_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1700-8","volume-title":"Intersection Theory","author":"W. Fulton","year":"1998","unstructured":"W. Fulton, Intersection Theory (Springer, Berlin, 1998)."},{"key":"9058_CR18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.7146\/math.scand.a-11489","volume":"33","author":"H.C. Hansen","year":"1973","unstructured":"H.C. Hansen, On cycles in flag manifolds, Math. Scand. 33, 269\u2013274 (1973).","journal-title":"Math. Scand."},{"key":"9058_CR19","series-title":"Research Notes in Mathematics","volume-title":"Geometry of Coxeter Groups","author":"H. Hiller","year":"1982","unstructured":"H. Hiller, Geometry of Coxeter Groups, Research Notes in Mathematics, vol.\u00a054 (Pitman Advanced Publishing Program, New York, 1982)."},{"key":"9058_CR20","series-title":"Graduated Texts in Math.","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6398-2","volume-title":"Introduction to Lie Algebras and Representation Theory","author":"J.E. Humphreys","year":"1972","unstructured":"J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduated Texts in Math., vol.\u00a09 (Springer, New York, 1972)."},{"key":"9058_CR21","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/0022-4049(74)90045-0","volume":"5","author":"D. Husemoller","year":"1974","unstructured":"D. Husemoller, J. Moore, J. Stasheff, Differential homological algebra and homogeneous spaces, J.\u00a0Pure Appl. Algebra 5, 113\u2013185 (1974).","journal-title":"J.\u00a0Pure Appl. Algebra"},{"key":"9058_CR22","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1112\/S0010437X04000788","volume":"141","author":"A. Iliev","year":"2005","unstructured":"A. Iliev, L. Manivel, The Chow ring of the Cayley plane, Compos. Math. 141, 146\u2013160 (2005).","journal-title":"Compos. Math."},{"issue":"2","key":"9058_CR23","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1215\/kjm\/1250522773","volume":"17","author":"K. Ishitoya","year":"1977","unstructured":"K. Ishitoya, Integral cohomology ring of the symmetric space EII, J.\u00a0Math. Kyoto Univ. 17(2), 375\u2013397 (1977).","journal-title":"J.\u00a0Math. Kyoto Univ."},{"key":"9058_CR24","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1215\/kjm\/1250522765","volume":"17","author":"K. Ishitoya","year":"1977","unstructured":"K. Ishitoya, H. Toda, On the cohomology of irreducible symmetric spaces of exceptional type, J.\u00a0Math. Kyoto Univ. 17, 225\u2013243 (1977).","journal-title":"J.\u00a0Math. Kyoto Univ."},{"key":"9058_CR25","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF01388548","volume":"80","author":"V.G. Kac","year":"1985","unstructured":"V.G. Kac, Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups, Invent. Math. 80, 69\u201379 (1985).","journal-title":"Invent. Math."},{"key":"9058_CR26","volume-title":"A User\u2019s Guide to Spectral Sequences","author":"J. McCleary","year":"2001","unstructured":"J. McCleary, A User\u2019s Guide to Spectral Sequences (Cambridge University Press, Cambridge, 2001)."},{"key":"9058_CR27","series-title":"Ann. Math. Studies","volume-title":"Characteristic Classes","author":"J. Milnor","year":"1975","unstructured":"J. Milnor, J. Stasheff, Characteristic Classes, Ann. Math. Studies, vol.\u00a076 (Princeton Univ. Press, Princeton, 1975)."},{"key":"9058_CR28","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1215\/kjm\/1250517635","volume":"41","author":"M. Nakagawa","year":"2001","unstructured":"M. Nakagawa, The integral cohomology ring of E 7\/T, J.\u00a0Math. Kyoto Univ. 41, 303\u2013321 (2001).","journal-title":"J.\u00a0Math. Kyoto Univ."},{"key":"9058_CR29","unstructured":"M. Nakagawa, The integral cohomology ring of E 8\/T 1\u22c5E 7, arXiv:math.AT\/0911.4793 ."},{"key":"9058_CR30","unstructured":"S.I. Nikolenko, N.S. Semenov, Chow ring structure made simple, arXiv:math.AG\/0606335 ."},{"key":"9058_CR31","series-title":"Studies in Advanced Mathematics","volume-title":"Algebra. A Computational Introduction","author":"J. Scherk","year":"2000","unstructured":"J. Scherk, Algebra. A Computational Introduction, Studies in Advanced Mathematics (Chapman & Hall\/CRC, Boca Raton, 2000)."},{"key":"9058_CR32","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1215\/kjm\/1250523124","volume":"15","author":"H. Toda","year":"1975","unstructured":"H. Toda, On the cohomology ring of some homogeneous spaces, J.\u00a0Math. Kyoto Univ. 15, 185\u2013199 (1975).","journal-title":"J.\u00a0Math. Kyoto Univ."},{"key":"9058_CR33","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1215\/kjm\/1250523239","volume":"14","author":"H. Toda","year":"1974","unstructured":"H. Toda, T. Watanabe, The integral cohomology ring of F 4\/T and E 6\/T, J.\u00a0Math. Kyoto Univ. 14, 257\u2013286 (1974).","journal-title":"J.\u00a0Math. Kyoto Univ."},{"key":"9058_CR34","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1215\/kjm\/1250523069","volume":"15","author":"T. Watanabe","year":"1975","unstructured":"T. Watanabe, The integral cohomology ring of the symmetric space EVII, J.\u00a0Math. Kyoto Univ. 15, 363\u2013385 (1975).","journal-title":"J.\u00a0Math. Kyoto Univ."},{"key":"9058_CR35","series-title":"Proceedings of Symposia in Pure Mathematics","first-page":"511","volume-title":"Group Representations: Cohomology, Group Actions and Topology","author":"T. Watanabe","year":"1998","unstructured":"T. Watanabe, Cohomology of the homogeneous space E 6\/T 1\u22c5SU(6), in Group Representations: Cohomology, Group Actions and Topology, Proceedings of Symposia in Pure Mathematics, vol.\u00a063 (AMS, Providence, 1998), pp.\u00a0511\u2013518."},{"issue":"2","key":"9058_CR36","doi-asserted-by":"crossref","first-page":"312","DOI":"10.2307\/2373822","volume":"99","author":"J. Wolf","year":"1977","unstructured":"J. Wolf, The cohomology of homogeneous spaces, Am. J. Math. 99(2), 312\u2013340 (1977).","journal-title":"Am. J. Math."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-010-9058-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-010-9058-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-010-9058-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T11:05:10Z","timestamp":1559127910000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-010-9058-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,6]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,6]]}},"alternative-id":["9058"],"URL":"https:\/\/doi.org\/10.1007\/s10208-010-9058-0","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,6]]}}}