Multiplicity one theorems

Name: Work Video:
Duration: 3 min 30 s
Description: In the local, characteristic 0, non-Archimedean case, we consider distributions on GL(n + 1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from GL(n + 1) to GL(n). Similar theorems are obtained for orthogonal or unitary groups.
Avraham Aizenbud; Dmitry Gourevitch; Stephen Rallis; Gérard Schiffmann
{'id': 'https://openalex.org/W2962906191', 'doi': 'https://doi.org/10.4007/annals.2010.172.1407', 'title': 'Multiplicity one theorems', 'display_name': 'Multiplicity one theorems', 'publication_year': 2010, 'publication_date': '2010-01-01', 'ids': {'openalex': 'https://openalex.org/W2962906191', 'doi': 'https://doi.org/10.4007/annals.2010.172.1407', 'mag': '2962906191'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.4007/annals.2010.172.1407', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S45918994', 'display_name': 'Annals of Mathematics', 'issn_l': '0003-486X', 'issn': ['0003-486X', '1939-8980'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310316273', 'host_organization_name': 'Princeton University', 'host_organization_lineage': ['https://openalex.org/P4310316273'], 'host_organization_lineage_names': ['Princeton University'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://doi.org/10.4007/annals.2010.172.1407', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5041197415', 'display_name': 'Avraham Aizenbud', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I53964585', 'display_name': 'Weizmann Institute of Science', 'ror': 'https://ror.org/0316ej306', 'country_code': 'IL', 'type': 'education', 'lineage': ['https://openalex.org/I53964585']}], 'countries': ['IL'], 'is_corresponding': False, 'raw_author_name': 'Avraham Aizenbud', 'raw_affiliation_strings': ['Faculty of Mathematics and Computer ScienceWeizmann Institute of\nSciencePOB 26Rehovot 76100Israel'], 'affiliations': [{'raw_affiliation_string': 'Faculty of Mathematics and Computer ScienceWeizmann Institute of\nSciencePOB 26Rehovot 76100Israel', 'institution_ids': ['https://openalex.org/I53964585']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5085710675', 'display_name': 'Dmitry Gourevitch', 'orcid': 'https://orcid.org/0000-0001-6436-2092'}, 'institutions': [{'id': 'https://openalex.org/I40036882', 'display_name': 'Institute for Advanced Study', 'ror': 'https://ror.org/00f809463', 'country_code': 'US', 'type': 'facility', 'lineage': ['https://openalex.org/I40036882']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Dmitry Gourevitch', 'raw_affiliation_strings': ['School of MathematicsIntitute for Advanced\nStudyEinstein DrivePrinceton, NJ 08540United States'], 'affiliations': [{'raw_affiliation_string': 'School of MathematicsIntitute for Advanced\nStudyEinstein DrivePrinceton, NJ 08540United States', 'institution_ids': ['https://openalex.org/I40036882']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5013975115', 'display_name': 'Stephen Rallis', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I52357470', 'display_name': 'The Ohio State University', 'ror': 'https://ror.org/00rs6vg23', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I52357470']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Stephen Rallis', 'raw_affiliation_strings': ['The Ohio State UniversityDepartment of Mathematics231 West 18th AvenueColumbus, OH 43210-1174United States'], 'affiliations': [{'raw_affiliation_string': 'The Ohio State UniversityDepartment of Mathematics231 West 18th AvenueColumbus, OH 43210-1174United States', 'institution_ids': ['https://openalex.org/I52357470']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5003705754', 'display_name': 'Gérard Schiffmann', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I1294671590', 'display_name': 'Centre National de la Recherche Scientifique', 'ror': 'https://ror.org/02feahw73', 'country_code': 'FR', 'type': 'government', 'lineage': ['https://openalex.org/I1294671590']}, {'id': 'https://openalex.org/I4210118362', 'display_name': 'Institut de Recherche Mathématique Avancée', 'ror': 'https://ror.org/02hwgty18', 'country_code': 'FR', 'type': 'facility', 'lineage': ['https://openalex.org/I1294671590', 'https://openalex.org/I4210118362', 'https://openalex.org/I4210141950', 'https://openalex.org/I68947357']}, {'id': 'https://openalex.org/I68947357', 'display_name': 'Université de Strasbourg', 'ror': 'https://ror.org/00pg6eq24', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I68947357']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Gérard Schiffmann', 'raw_affiliation_strings': ['Institut de Recherche Mathématique\nAvancéeUniversité de Strasbourg et\nCNRS7 rue René-Descartes67084 Strasbourg CedexFrance'], 'affiliations': [{'raw_affiliation_string': 'Institut de Recherche Mathématique\nAvancéeUniversité de Strasbourg et\nCNRS7 rue René-Descartes67084 Strasbourg CedexFrance', 'institution_ids': ['https://openalex.org/I1294671590', 'https://openalex.org/I4210118362', 'https://openalex.org/I68947357']}]}], 'institution_assertions': [], 'countries_distinct_count': 3, 'institutions_distinct_count': 6, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 15.586, 'has_fulltext': False, 'cited_by_count': 202, 'citation_normalized_percentile': {'value': 0.999768, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 98, 'max': 99}, 'biblio': {'volume': '172', 'issue': '2', 'first_page': '1407', 'last_page': '1407'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11680', 'display_name': 'Advanced Algebra and Geometry', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11680', 'display_name': 'Advanced Algebra and Geometry', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T13234', 'display_name': 'advanced mathematical theories', 'score': 0.993, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11210', 'display_name': 'Mathematical Analysis and Transform Methods', 'score': 0.9782, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/multiplicity', 'display_name': 'Multiplicity (mathematics)', 'score': 0.74693024}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.9485903}, {'id': 'https://openalex.org/C156004811', 'wikidata': 'https://www.wikidata.org/wiki/Q2228257', 'display_name': 'Multiplicity (mathematics)', 'level': 2, 'score': 0.74693024}, {'id': 'https://openalex.org/C67820243', 'wikidata': 'https://www.wikidata.org/wiki/Q179164', 'display_name': 'Unitary state', 'level': 2, 'score': 0.71291876}, {'id': 'https://openalex.org/C190470478', 'wikidata': 'https://www.wikidata.org/wiki/Q2370229', 'display_name': 'Invariant (physics)', 'level': 2, 'score': 0.70763344}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.56123877}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.27265579}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.13156849}, {'id': 'https://openalex.org/C17744445', 'wikidata': 'https://www.wikidata.org/wiki/Q36442', 'display_name': 'Political science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199539241', 'wikidata': 'https://www.wikidata.org/wiki/Q7748', 'display_name': 'Law', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.4007/annals.2010.172.1407', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S45918994', 'display_name': 'Annals of Mathematics', 'issn_l': '0003-486X', 'issn': ['0003-486X', '1939-8980'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310316273', 'host_organization_name': 'Princeton University', 'host_organization_lineage': ['https://openalex.org/P4310316273'], 'host_organization_lineage_names': ['Princeton University'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/0709.4215', 'pdf_url': 'http://arxiv.org/pdf/0709.4215', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.4007/annals.2010.172.1407', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S45918994', 'display_name': 'Annals of Mathematics', 'issn_l': '0003-486X', 'issn': ['0003-486X', '1939-8980'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310316273', 'host_organization_name': 'Princeton University', 'host_organization_lineage': ['https://openalex.org/P4310316273'], 'host_organization_lineage_names': ['Princeton University'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 20, 'referenced_works': ['https://openalex.org/W1511916494', 'https://openalex.org/W1519146779', 'https://openalex.org/W1527902516', 'https://openalex.org/W1574274213', 'https://openalex.org/W1639250485', 'https://openalex.org/W1837911550', 'https://openalex.org/W1890231692', 'https://openalex.org/W1981306886', 'https://openalex.org/W1984807317', 'https://openalex.org/W2026039439', 'https://openalex.org/W2033740602', 'https://openalex.org/W2046239715', 'https://openalex.org/W2077242410', 'https://openalex.org/W2088825391', 'https://openalex.org/W2574785083', 'https://openalex.org/W2579515327', 'https://openalex.org/W2951970695', 'https://openalex.org/W3101562167', 'https://openalex.org/W3124815093', 'https://openalex.org/W622826425'], 'related_works': ['https://openalex.org/W4245490552', 'https://openalex.org/W4225152035', 'https://openalex.org/W3002753104', 'https://openalex.org/W2277771903', 'https://openalex.org/W2082458642', 'https://openalex.org/W2077600819', 'https://openalex.org/W2061531152', 'https://openalex.org/W2007980826', 'https://openalex.org/W1979597421', 'https://openalex.org/W1587224694'], 'abstract_inverted_index': {'In': [0], 'the': [1, 18], 'local,': [2], 'characteristic': [3], '0,': [4], 'non-Archimedean': [5], 'case,': [6], 'we': [7], 'consider': [8], 'distributions': [9, 27], 'on': [10], 'GL(n': [11, 41], '+': [12, 42], '1)': [13, 43], 'which': [14], 'are': [15, 28, 48], 'invariant': [16, 29], 'under': [17], 'adjoint': [19], 'action': [20], 'of': [21], 'GL(n).': [22, 45], 'We': [23], 'prove': [24], 'that': [25], 'such': [26], 'by': [30], 'transposition.': [31], 'This': [32], 'implies': [33], 'multiplicity': [34], 'at': [35], 'most': [36], 'one': [37], 'for': [38, 50], 'restrictions': [39], 'from': [40], 'to': [44], 'Similar': [46], 'theorems': [47], 'obtained': [49], 'orthogonal': [51], 'or': [52], 'unitary': [53], 'groups.': [54]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2962906191', 'counts_by_year': [{'year': 2024, 'cited_by_count': 3}, {'year': 2023, 'cited_by_count': 5}, {'year': 2022, 'cited_by_count': 5}, {'year': 2021, 'cited_by_count': 24}, {'year': 2020, 'cited_by_count': 12}, {'year': 2019, 'cited_by_count': 14}, {'year': 2018, 'cited_by_count': 10}, {'year': 2017, 'cited_by_count': 12}, {'year': 2016, 'cited_by_count': 14}, {'year': 2015, 'cited_by_count': 18}, {'year': 2014, 'cited_by_count': 20}, {'year': 2013, 'cited_by_count': 20}, {'year': 2012, 'cited_by_count': 17}], 'updated_date': '2024-12-19T07:33:39.888276', 'created_date': '2019-07-30'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
