335:
206:
509:) states that two cuspidal automorphic representations of the general linear group are isomorphic if their local components are isomorphic for all but a finite number of places.
854:
839:
749:
Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1
761:
598:
330:{\displaystyle L_{0}^{2}(G(K)\backslash G(\mathbf {A} ),\omega )={\widehat {\bigoplus }}_{(\pi ,V_{\pi })}m_{\pi }V_{\pi }}
518:
849:
692:
633:
753:
590:
537:
198:
844:
341:
43:
20:
384:
50:
35:
134:
684:
625:
186:
137:
747:
32:
786:
380:
28:
823:
771:
729:
670:
608:
566:
467:
427:
54:
39:
8:
58:
811:
717:
658:
803:
757:
709:
650:
594:
554:
344:
120:
795:
701:
642:
546:
819:
767:
725:
666:
604:
584:
562:
463:
451:
833:
807:
713:
654:
558:
626:"On Euler products and the classification of automorphic representations. I"
743:
97:
81:
815:
721:
662:
550:
108:
38:. The multiplicity in question is the number of times a given abstract
575:"Lectures on L-functions, converse theorems, and functoriality for GL
396:
799:
705:
646:
574:
685:"On Euler products and the classification of automorphic forms. II"
65:
742:
Piatetski-Shapiro, I. I. (1979), "Multiplicity one theorems", in
583:, in Cogdell, James W.; Kim, Henry H.; Murty, Maruti Ram (eds.),
357:
49:
A multiplicity one theorem may also refer to a result about the
619:, Lecture Notes in Mathematics, vol. 114, Springer-Verlag
778:
Shalika, J. A. (1974), "The multiplicity one theorem for GL
589:, Fields Inst. Monogr., vol. 20, Providence, R.I.:
395:) occurs with multiplicity at most one in the space of
752:, Proc. Sympos. Pure Math., XXXIII, Providence, R.I.:
240:
209:
438:), has the multiplicity-one property was proved by
492:
329:
741:
498:
447:
187:space of cusp forms with central character ω
831:
614:
439:
682:
623:
531:Blasius, Don (1994), "On multiplicities for SL(
506:
502:
462: > 2 using the uniqueness of the
615:Jacquet, Hervé; Langlands, Robert (1970),
777:
572:
530:
497:The strong multiplicity one theorem of
486:
455:
832:
501:and Jacquet and Shalika (
96:be a reductive algebraic group over a
683:Jacquet, H.; Shalika, J. A. (1981b),
624:Jacquet, H.; Shalika, J. A. (1981a),
446: = 2 and independently by
586:Lectures on automorphic L-functions
273:
42:is realised in a certain space, of
13:
466:. Multiplicity-one also holds for
14:
866:
855:Theorems in representation theory
250:
197:). This space decomposes into a
840:Representation theory of groups
693:American Journal of Mathematics
634:American Journal of Mathematics
493:Strong multiplicity one theorem
440:Jacquet & Langlands (1970)
363:The group of adelic points of
302:
283:
263:
254:
246:
237:
231:
225:
19:In the mathematical theory of
1:
754:American Mathematical Society
591:American Mathematical Society
538:Israel Journal of Mathematics
524:
87:
72:. In that context, the pair (
414:is 0 or 1 for all such
199:direct sum of Hilbert spaces
7:
519:Gan-Gross-Prasad conjecture
512:
46:, given in a concrete way.
44:square-integrable functions
21:automorphic representations
10:
871:
617:Automorphic forms on GL(2)
573:Cogdell, James W. (2004),
421:
399:of central character
375:), is said to satisfy the
850:Theorems in number theory
746:; Casselman., W. (eds.),
385:admissible representation
377:multiplicity-one property
36:reductive algebraic group
499:Piatetski-Shapiro (1979)
448:Piatetski-Shapiro (1979)
25:multiplicity-one theorem
340:where the sum is over
331:
27:is a result about the
787:Annals of Mathematics
332:
80:) is called a strong
29:representation theory
756:, pp. 209–212,
428:general linear group
207:
40:group representation
16:Mathematical theorem
485: > 2 (
224:
551:10.1007/BF02937513
426:The fact that the
345:subrepresentations
327:
210:
845:Automorphic forms
790:, Second Series,
763:978-0-8218-1435-2
600:978-0-8218-3516-6
593:, pp. 1–96,
356:are non-negative
279:
138:unitary character
862:
826:
774:
738:
737:
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864:
863:
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860:
859:
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800:10.2307/1971071
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734:
732:
706:10.2307/2374050
687:
675:
673:
647:10.2307/2374103
628:
601:
580:
527:
515:
495:
464:Whittaker model
424:
415:
413:
410:
400:
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352:
321:
317:
311:
307:
296:
292:
282:
271:
270:
269:
249:
219:
214:
208:
205:
204:
180:
162:
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868:
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857:
852:
847:
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827:
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700:(4): 777–815,
680:
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570:
545:(1): 237–251,
526:
523:
522:
521:
514:
511:
494:
491:
473:, but not for
423:
420:
409:
351:
338:
337:
324:
320:
314:
310:
304:
299:
295:
291:
288:
285:
278:
275:
268:
265:
262:
259:
256:
252:
248:
245:
242:
239:
236:
233:
230:
227:
222:
217:
213:
160:
89:
86:
55:representation
15:
9:
6:
4:
3:
2:
867:
856:
853:
851:
848:
846:
843:
841:
838:
837:
835:
825:
821:
817:
813:
809:
805:
801:
797:
793:
789:
788:
782:
776:
773:
769:
765:
759:
755:
751:
750:
745:
744:Borel, Armand
740:
731:
727:
723:
719:
715:
711:
707:
703:
699:
695:
694:
686:
681:
672:
668:
664:
660:
656:
652:
648:
644:
640:
636:
635:
627:
622:
618:
613:
610:
606:
602:
596:
592:
588:
587:
582:
579:
571:
568:
564:
560:
556:
552:
548:
544:
540:
539:
534:
529:
528:
520:
517:
516:
510:
508:
504:
500:
490:
488:
484:
480:
476:
472:
470:
465:
461:
457:
453:
449:
445:
441:
437:
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429:
419:
408:
403:
398:
394:
390:
386:
382:
378:
374:
370:
366:
361:
359:
350:
346:
343:
322:
318:
312:
308:
297:
293:
289:
286:
276:
266:
260:
257:
243:
234:
228:
220:
215:
211:
203:
202:
201:
200:
196:
192:
188:
185:) denote the
183:
178:
174:
170:
166:
159:
155:
151:
147:
143:
139:
136:
131:
126:
122:
118:
114:
110:
106:
102:
99:
95:
85:
83:
79:
75:
71:
67:
63:
60:
56:
52:
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41:
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34:
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22:
791:
785:
780:
748:
733:, retrieved
697:
691:
674:, retrieved
638:
632:
616:
585:
577:
542:
536:
532:
496:
487:Blasius 1994
482:
478:
474:
468:
459:
443:
435:
431:
425:
406:
401:
392:
388:
383:irreducible
376:
372:
368:
364:
362:
348:
339:
194:
190:
181:
176:
172:
168:
164:
157:
153:
149:
145:
141:
129:
124:
116:
112:
104:
100:
98:number field
93:
91:
82:Gelfand pair
77:
73:
69:
61:
48:
24:
18:
794:: 171–193,
342:irreducible
119:denote the
107:denote the
51:restriction
834:Categories
735:2021-08-06
676:2021-08-06
525:References
397:cusp forms
135:continuous
88:Definition
808:0003-486X
714:0002-9327
655:0002-9327
559:0021-2172
323:π
313:π
298:π
287:π
277:^
274:⨁
261:ω
241:∖
513:See also
358:integers
179:),
127:and let
103:and let
66:subgroup
824:0348047
816:1971071
772:0546599
730:0618323
722:2374050
671:0618323
663:2374103
609:2071506
567:1303497
454: (
452:Shalika
422:Results
405:, i.e.
379:if any
76:,
822:
814:
806:
770:
760:
728:
720:
712:
669:
661:
653:
607:
597:
565:
557:
481:) for
458:) for
381:smooth
156:. Let
121:centre
115:. Let
109:adeles
68:
33:adelic
31:of an
812:JSTOR
718:JSTOR
688:(PDF)
659:JSTOR
629:(PDF)
507:1981b
503:1981a
152:) to
140:from
133:be a
64:to a
59:group
57:of a
53:of a
804:ISSN
758:ISBN
710:ISSN
651:ISSN
595:ISBN
555:ISSN
535:)",
456:1974
450:and
442:for
347:and
148:)\Z(
92:Let
23:, a
796:doi
792:100
784:",
702:doi
698:103
643:doi
639:103
547:doi
489:).
471:(2)
387:of
189:on
123:of
111:of
836::
820:MR
818:,
810:,
802:,
768:MR
766:,
726:MR
724:,
716:,
708:,
696:,
690:,
667:MR
665:,
657:,
649:,
637:,
631:,
605:MR
603:,
563:MR
561:,
553:,
543:88
541:,
505:,
475:SL
469:SL
432:GL
430:,
418:.
367:,
360:.
171:)/
84:.
798::
781:n
704::
645::
581:"
578:n
549::
533:n
483:n
479:n
477:(
460:n
444:n
436:n
434:(
416:π
411:π
407:m
402:ω
393:A
391:(
389:G
373:A
371:(
369:G
365:G
353:π
349:m
319:V
309:m
303:)
294:V
290:,
284:(
267:=
264:)
258:,
255:)
251:A
247:(
244:G
238:)
235:K
232:(
229:G
226:(
221:2
216:0
212:L
195:A
193:(
191:G
182:ω
177:A
175:(
173:G
169:K
167:(
165:G
163:(
161:0
158:L
154:C
150:A
146:K
144:(
142:Z
130:ω
125:G
117:Z
113:K
105:A
101:K
94:G
78:H
74:G
70:H
62:G
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