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Weakly symmetric space

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472: 47:, the symmetric case being when the isometry is required to have period two. The classification of weakly symmetric spaces relies on that of periodic automorphisms of complex 513: 506: 303:(1956), "Harmonic analysis and discontinuous groups in weakly symmetric riemannian spaces, with applications to Dirichlet series", 444: 557: 499: 272:
Mikityuk, I. V. (1987), "On the integrability of invariant Hamiltonian systems with homogeneous configuration spaces",
135: 114: 419: 532: 537: 547: 155:"Geometry of multiplicity-free representations of GL(n), visible actions on flag varieties, and triunity" 552: 248: 56: 318: 487: 185:
Kobayashi, Toshiyuki (2007), "A generalized Cartan decomposition for the double coset space (U(n
243: 212: 48: 417:
Wolf, J. A.; Gray, A. (1968), "Homogeneous spaces defined by Lie group automorphisms. I, II",
479: 210:
Krämer, Manfred (1979), "Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen",
356:
Stembridge, J. R. (2003), "Multiplicity-free products and restrictions of Weyl characters",
390: 281: 234:
Matsuki, Toshihiko (2013), "An example of orthogonal triple flag variety of finite type",
8: 542: 170: 40: 394: 285: 406: 345: 261: 174: 94: 440: 410: 265: 131: 110: 98: 60: 402: 349: 293: 178: 398: 365: 335: 327: 289: 257: 253: 166: 86: 370: 32: 227:
Proceedings of the International Congress of Mathematicians, Vol. II, 1990 Kyoto
483: 378: 74: 381:(2001), "Commutative homogeneous spaces and co-isotropic symplectic actions", 331: 144:
Kobayashi, Toshiyuki (2002). "Branching problems of unitary representations".
36: 526: 458: 316:
Stembridge, J. R. (2001), "Multiplicity-free products of Schur functions",
300: 52: 28: 432: 340: 20: 457:, Progr. Nonlinear Differential Equations Appl., vol. 20, Boston: 123: 90: 154: 146:
Proceedings of the International Congress of Mathematicians, Vol. II
44: 471: 77:(1999), "Weakly symmetric spaces and spherical varieties", 63:, known for symmetric spaces, has not yet been developed. 225:
Matsuki, Toshihiko (1991), "Orbits on flag manifolds",
107:
Differential geometry, Lie groups and symmetric spaces
27:
is a notion introduced by the Norwegian mathematician
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Ziller, Wolfgang (1996), "Weakly symmetric spaces",
39:. Geometrically the spaces are defined as complete 524: 43:such that any two points can be exchanged by an 72: 148:. Beijing: Higher Ed. Press. pp. 615–627. 507: 130:(3rd ed.), Cambridge University Press, 514: 500: 355: 315: 369: 339: 247: 184: 152: 143: 416: 271: 104: 437:Harmonic Analysis on Commutative Spaces 377: 299: 233: 224: 55:, although the corresponding theory of 525: 452: 209: 466: 431: 229:, Math. Soc. Japan, pp. 807–813 31:in the 1950s as a generalisation of 122: 13: 171:10.1023/B:ACAP.0000024198.46928.0c 14: 569: 439:, American Mathematical Society, 128:Infinite dimensional Lie algebras 470: 420:Journal of Differential Geometry 403:10.1070/RM2001v056n01ABEH000356 294:10.1070/SM1987v057n02ABEH003084 258:10.1016/j.jalgebra.2012.11.012 16:Geometry notion in mathematics 1: 371:10.1090/S1088-4165-03-00150-X 153:Kobayashi, Toshiyuki (2004), 66: 486:. You can help Knowledge by 7: 558:Differential geometry stubs 105:Helgason, Sigurdur (1978), 51:. They provide examples of 10: 574: 465: 332:10.1007/s00026-001-8008-6 319:Annals of Combinatorics 305:J. Indian Math. Society 49:semisimple Lie algebras 482:-related article is a 213:Compositio Mathematica 197:))\U(n)/(U(p)Ă—U(q))", 25:weakly symmetric space 533:Differential geometry 480:differential geometry 383:Russian Math. Surveys 358:Representation Theory 41:Riemannian manifolds 538:Riemannian geometry 395:2001RuMaS..56....1V 286:1987SbMat..57..527M 57:spherical functions 548:Homogeneous spaces 461:, pp. 355–368 455:Topics in geometry 274:Math. USSR Sbornik 199:J. Math. Soc. Jpn. 109:, Academic Press, 91:10.1007/BF01236659 553:Harmonic analysis 495: 494: 446:978-0-8218-4289-8 427:: 77–114, 115–159 73:Akhiezer, D. N.; 61:harmonic analysis 565: 516: 509: 502: 474: 467: 462: 449: 428: 413: 374: 373: 352: 343: 312: 296: 268: 251: 230: 221: 206: 181: 159:Acta Appl. Math. 149: 140: 119: 101: 573: 572: 568: 567: 566: 564: 563: 562: 523: 522: 521: 520: 447: 364:(18): 404–439, 249:10.1.1.750.7197 196: 192: 188: 138: 117: 69: 33:symmetric space 17: 12: 11: 5: 571: 561: 560: 555: 550: 545: 540: 535: 519: 518: 511: 504: 496: 493: 492: 475: 464: 463: 450: 445: 429: 414: 379:Vinberg, É. B. 375: 353: 326:(2): 113–121, 313: 297: 280:(2): 527–546, 269: 231: 222: 207: 194: 190: 186: 182: 150: 141: 136: 120: 115: 102: 79:Transf. Groups 75:Vinberg, E. B. 68: 65: 15: 9: 6: 4: 3: 2: 570: 559: 556: 554: 551: 549: 546: 544: 541: 539: 536: 534: 531: 530: 528: 517: 512: 510: 505: 503: 498: 497: 491: 489: 485: 481: 476: 473: 469: 468: 460: 456: 451: 448: 442: 438: 434: 430: 426: 422: 421: 415: 412: 408: 404: 400: 396: 392: 388: 384: 380: 376: 372: 367: 363: 359: 354: 351: 347: 342: 341:2027.42/41839 337: 333: 329: 325: 321: 320: 314: 310: 306: 302: 298: 295: 291: 287: 283: 279: 275: 270: 267: 263: 259: 255: 250: 245: 241: 237: 232: 228: 223: 219: 216:(in German), 215: 214: 208: 204: 200: 183: 180: 176: 172: 168: 164: 160: 156: 151: 147: 142: 139: 137:0-521-46693-8 133: 129: 125: 121: 118: 116:0-12-338460-5 112: 108: 103: 100: 96: 92: 88: 84: 80: 76: 71: 70: 64: 62: 58: 54: 53:Gelfand pairs 50: 46: 42: 38: 34: 30: 26: 22: 488:expanding it 477: 454: 436: 424: 418: 386: 382: 361: 357: 323: 317: 308: 304: 277: 273: 239: 235: 226: 217: 211: 202: 198: 162: 158: 145: 127: 106: 82: 78: 29:Atle Selberg 24: 18: 433:Wolf, J. A. 389:(1): 1–60, 301:Selberg, A. 242:: 148–187, 165:: 129–146, 37:Élie Cartan 21:mathematics 543:Lie groups 527:Categories 459:Birkhäuser 236:J. Algebra 124:Kac, V. G. 67:References 411:250919435 266:119132477 244:CiteSeerX 220:: 129–153 205:: 669–691 99:124032062 35:, due to 435:(2007), 350:18105235 179:14530010 126:(1990), 85:: 3–24, 45:isometry 391:Bibcode 311:: 47–87 282:Bibcode 443:  409:  348:  264:  246:  177:  134:  113:  97:  478:This 407:S2CID 346:S2CID 262:S2CID 193:)Ă—U(n 189:)Ă—U(n 175:S2CID 95:S2CID 484:stub 441:ISBN 132:ISBN 111:ISBN 23:, a 399:doi 366:doi 336:hdl 328:doi 290:doi 254:doi 240:375 167:doi 87:doi 59:in 19:In 529:: 423:, 405:, 397:, 387:56 385:, 360:, 344:, 334:, 322:, 309:20 307:, 288:, 278:57 276:, 260:, 252:, 238:, 218:38 203:59 201:, 173:, 163:81 161:, 157:, 93:, 81:, 515:e 508:t 501:v 490:. 425:2 401:: 393:: 368:: 362:7 338:: 330:: 324:5 292:: 284:: 256:: 195:3 191:2 187:1 169:: 89:: 83:4

Index

mathematics
Atle Selberg
symmetric space
Élie Cartan
Riemannian manifolds
isometry
semisimple Lie algebras
Gelfand pairs
spherical functions
harmonic analysis
Vinberg, E. B.
doi
10.1007/BF01236659
S2CID
124032062
ISBN
0-12-338460-5
Kac, V. G.
ISBN
0-521-46693-8
"Geometry of multiplicity-free representations of GL(n), visible actions on flag varieties, and triunity"
doi
10.1023/B:ACAP.0000024198.46928.0c
S2CID
14530010
Compositio Mathematica
CiteSeerX
10.1.1.750.7197
doi
10.1016/j.jalgebra.2012.11.012

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