{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:21:45Z","timestamp":1775053305360,"version":"3.50.1"},"reference-count":33,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2004,2,1]],"date-time":"2004-02-01T00:00:00Z","timestamp":1075593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3490,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["European Journal of Combinatorics"],"published-print":{"date-parts":[[2004,2]]},"DOI":"10.1016\/s0195-6698(03)00101-x","type":"journal-article","created":{"date-parts":[[2003,9,16]],"date-time":"2003-09-16T22:32:50Z","timestamp":1063751570000},"page":"213-227","source":"Crossref","is-referenced-by-count":9,"title":["Spherical designs and finite group representations (some results of E. Bannai)"],"prefix":"10.1016","volume":"25","author":[{"given":"Pierre de la","family":"Harpe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claude","family":"Pache","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0195-6698(03)00101-X_B1","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/BF01298830","article-title":"A generalized mean-value theorem","volume":"106","author":"Arias de Reyna","year":"1988","journal-title":"Mh. Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B2","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/S0195-6698(13)80013-3","article-title":"Construction of designs on the 2-sphere","volume":"12","author":"Bajnok","year":"1991","journal-title":"European J. Combin."},{"key":"10.1016\/S0195-6698(03)00101-X_B3","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF00147866","article-title":"Construction of spherical t-designs","volume":"43","author":"Bajnok","year":"1992","journal-title":"Geom. Dedicata"},{"key":"10.1016\/S0195-6698(03)00101-X_B4","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0097-3165(79)90064-5","article-title":"On some spherical t-designs","volume":"26","author":"Bannai","year":"1979","journal-title":"J. Combin. Theory, Ser. A"},{"key":"10.1016\/S0195-6698(03)00101-X_B5","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1090\/pspum\/037\/604622","article-title":"Orthogonal polynomials, algebraic combinatorics and spherical t-designs","volume":"37","author":"Bannai","year":"1980","journal-title":"Proc. Sympos. Pure Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B6","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2969\/jmsj\/03620341","article-title":"Spherical t-designs which are orbits of finite groups","volume":"36","author":"Bannai","year":"1984","journal-title":"J. Math. Soc. Japan"},{"key":"10.1016\/S0195-6698(03)00101-X_B7","doi-asserted-by":"crossref","unstructured":"E. Bannai, Spherical designs and group representations, in: C. Greene (Ed.), Combinatorics and Algebra, Contemporary Mathematics, vol.\u00a034, 1984, pp.\u00a095\u2013107","DOI":"10.1090\/conm\/034\/777697"},{"key":"10.1016\/S0195-6698(03)00101-X_B8","series-title":"Groupes et alg\u00e8bres de Lie","author":"Bourbaki","year":"1968"},{"key":"10.1016\/S0195-6698(03)00101-X_B9","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF03187604","article-title":"Spherical codes and designs","volume":"6","author":"Delsarte","year":"1977","journal-title":"Geom. Dedicata"},{"key":"10.1016\/S0195-6698(03)00101-X_B10","first-page":"493","article-title":"Uber den von L. Bieberbach gefundenen Beweis eines Satzes von C. Jordan","volume":"III","author":"Frobenius","year":"1911","journal-title":"Gesammelte Abhandlungen"},{"key":"10.1016\/S0195-6698(03)00101-X_B11","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1090\/pspum\/034\/525330","article-title":"Spherical designs","volume":"34","author":"Goethals","year":"1979","journal-title":"Proc. Sympos. Pure Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B12","series-title":"The Geometric Vein, the Coxeter Festschrift","first-page":"203","article-title":"Cubature formulae, polytopes, and spherical designs","author":"Goethals","year":"1981"},{"key":"10.1016\/S0195-6698(03)00101-X_B13","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1090\/S0894-0347-1990-1071117-8","article-title":"Group representations and lattices","volume":"3","author":"Gross","year":"1990","journal-title":"J. Amer. Math. Soc."},{"key":"10.1016\/S0195-6698(03)00101-X_B14","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/S0764-4442(01)02142-5","article-title":"Groupes engendr\u00e9s par des r\u00e9flexions, designs sph\u00e9riques et r\u00e9seau de Leech","volume":"333, S\u00e9r. I","author":"de la Harpe","year":"2001","journal-title":"C.R. Acad. Sci. Paris"},{"key":"10.1016\/S0195-6698(03)00101-X_B15","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/0001-8708(79)90038-0","article-title":"Most primitive groups have messy invariants","volume":"32","author":"Huffman","year":"1979","journal-title":"Adv. Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B16","series-title":"Reflection Groups and Coxeter Groups","author":"Humphreys","year":"1990"},{"key":"10.1016\/S0195-6698(03)00101-X_B17","first-page":"834","article-title":"A mass formula for unimodular lattices with no roots","volume":"72","author":"King","year":"2003","journal-title":"Mathematics of Computation"},{"key":"10.1016\/S0195-6698(03)00101-X_B18","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1006\/jabr.2000.8713","article-title":"Symmetric squares, spherical designs, and lattice minima","volume":"240","author":"Lempken","year":"2001","journal-title":"J. Algebra"},{"key":"10.1016\/S0195-6698(03)00101-X_B19","doi-asserted-by":"crossref","first-page":"379","DOI":"10.2140\/pjm.2002.202.379","article-title":"Irreducibility of tensor squares, symmetric squares and alternating squares","volume":"202","author":"Magaard","year":"2002","journal-title":"Pacific J. Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B20","doi-asserted-by":"crossref","unstructured":"J. Martinet, Les r\u00e9seaux parfaits des espaces euclidiens, Masson, 1996 (English Trans.: Perfect Lattices in Euclidean Spaces, Springer-Verlag, 2003)","DOI":"10.1007\/978-3-662-05167-2"},{"key":"10.1016\/S0195-6698(03)00101-X_B21","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0001-8708(84)90022-7","article-title":"Averaging sets: a generalization of mean values and spherical designs","volume":"152","author":"Seymour","year":"1984","journal-title":"Adv. Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B22","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1023\/A:1018723416627","article-title":"Spherical 7-designs in 2n-dimensional Euclidean spaces","volume":"10","author":"Sidelnikov","year":"1999","journal-title":"J. Algebraic Combin."},{"issue":"4","key":"10.1016\/S0195-6698(03)00101-X_B23","first-page":"673","article-title":"Orbital spherical 11-designs whose initial point is a root of an invariant polynomial","volume":"11","author":"Sidelnikov","year":"2000","journal-title":"St. Petersburg Math. J."},{"key":"10.1016\/S0195-6698(03)00101-X_B24","doi-asserted-by":"crossref","first-page":"82","DOI":"10.2307\/2319929","article-title":"Error-correcting codes and invariant theory: new applications of a nineteenth-century technique","volume":"84","author":"Sloane","year":"1977","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/S0195-6698(03)00101-X_B25","first-page":"1307","article-title":"Cubature formulas on the sphere invariant under finite groups of rotations","volume":"3","author":"Sobolev","year":"1962","journal-title":"Soviet Math. Dokl."},{"key":"10.1016\/S0195-6698(03)00101-X_B26","series-title":"Introduction to Fourier Analysis on Euclidean Spaces","author":"Stein","year":"1971"},{"key":"10.1016\/S0195-6698(03)00101-X_B27","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/0021-8693(76)90234-9","article-title":"Finite groups and lattices","volume":"38","author":"Thompson","year":"1976","journal-title":"J. Algebra"},{"key":"10.1016\/S0195-6698(03)00101-X_B28","first-page":"47","article-title":"On even unimodular extremal lattices","volume":"165","author":"Venkov","year":"1985","journal-title":"Proc. Steklov Inst. Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B29","unstructured":"B. Venkov (Notes par J. Martinet), R\u00e9seaux et designs sph\u00e9riques, R\u00e9seaux euclidiens, designs sph\u00e9riques et formes modulaires, Monographie de l\u2019Enseignement math\u00e9matique 37 (2001) 10\u201386"},{"key":"10.1016\/S0195-6698(03)00101-X_B30","article-title":"Special functions and the theory of group representations","volume":"vol. 22","author":"Vilenkin","year":"1968"},{"key":"10.1016\/S0195-6698(03)00101-X_B31","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF01299278","article-title":"On averaging sets","volume":"111","author":"Wagner","year":"1991","journal-title":"Mh. Math."},{"key":"10.1016\/S0195-6698(03)00101-X_B32","doi-asserted-by":"crossref","first-page":"5278","DOI":"10.1073\/pnas.81.16.5278","article-title":"Post-classification version of Jordan\u2019s theorem on finite linear groups","volume":"81","author":"Weisfeiler","year":"1984","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"10.1016\/S0195-6698(03)00101-X_B33","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970470","article-title":"Orthogonal polynomial and special functions","author":"Askey","year":"1975"}],"container-title":["European Journal of Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S019566980300101X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S019566980300101X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T23:07:55Z","timestamp":1682550475000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S019566980300101X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,2]]}},"alternative-id":["S019566980300101X"],"URL":"https:\/\/doi.org\/10.1016\/s0195-6698(03)00101-x","relation":{},"ISSN":["0195-6698"],"issn-type":[{"value":"0195-6698","type":"print"}],"subject":[],"published":{"date-parts":[[2004,2]]}}}