Quiver Varieties and Branching
Braverman and Finkelberg recently proposed the geometric Satake correspondence for the affine Kac-Moody group Gaff [Braverman A., Finkelberg M., arXiv:0711.2083]. They conjecture that intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of Gcpt-instantons on R...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149260 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quiver Varieties and Branching / H. Nakajima // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862667032205459456 |
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| author | Nakajima, H. |
| author_facet | Nakajima, H. |
| citation_txt | Quiver Varieties and Branching / H. Nakajima // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Braverman and Finkelberg recently proposed the geometric Satake correspondence for the affine Kac-Moody group Gaff [Braverman A., Finkelberg M., arXiv:0711.2083]. They conjecture that intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of Gcpt-instantons on R4/Zr correspond to weight spaces of representations of the Langlands dual group GaffÚ at level r. When G = SL(l), the Uhlenbeck compactification is the quiver variety of type sl(r)aff, and their conjecture follows from the author's earlier result and I. Frenkel's level-rank duality. They further introduce a convolution diagram which conjecturally gives the tensor product multiplicity [Braverman A., Finkelberg M., Private communication, 2008]. In this paper, we develop the theory for the branching in quiver varieties and check this conjecture for G = SL(l).
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| first_indexed | 2025-12-07T15:21:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149260 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:21:08Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Nakajima, H. 2019-02-19T19:29:30Z 2019-02-19T19:29:30Z 2009 Quiver Varieties and Branching / H. Nakajima // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B65; 14D21 https://nasplib.isofts.kiev.ua/handle/123456789/149260 Braverman and Finkelberg recently proposed the geometric Satake correspondence for the affine Kac-Moody group Gaff [Braverman A., Finkelberg M., arXiv:0711.2083]. They conjecture that intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of Gcpt-instantons on R4/Zr correspond to weight spaces of representations of the Langlands dual group GaffÚ at level r. When G = SL(l), the Uhlenbeck compactification is the quiver variety of type sl(r)aff, and their conjecture follows from the author's earlier result and I. Frenkel's level-rank duality. They further introduce a convolution diagram which conjecturally gives the tensor product multiplicity [Braverman A., Finkelberg M., Private communication, 2008]. In this paper, we develop the theory for the branching in quiver varieties and check this conjecture for G = SL(l). This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. This work is supported by the Grant-in-aid for Scientific Research (No.19340006), JSPS. This work was started while the author was visiting the Institute for Advanced Study with supports by the Ministry of Education, Japan and the Friends of the Institute. The author would like to thank to A. Braverman and M. Finkelberg for discussion on the subject, and to the referees for their careful readings and comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quiver Varieties and Branching Article published earlier |
| spellingShingle | Quiver Varieties and Branching Nakajima, H. |
| title | Quiver Varieties and Branching |
| title_full | Quiver Varieties and Branching |
| title_fullStr | Quiver Varieties and Branching |
| title_full_unstemmed | Quiver Varieties and Branching |
| title_short | Quiver Varieties and Branching |
| title_sort | quiver varieties and branching |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149260 |
| work_keys_str_mv | AT nakajimah quivervarietiesandbranching |