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
Datum:2009
1. Verfasser: Nakajima, H.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2009
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
id nasplib_isofts_kiev_ua-123456789-149260
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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Quiver Varieties and Branching
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Quiver Varieties and Branching
spellingShingle Quiver Varieties and Branching
Nakajima, H.
title_short Quiver Varieties and Branching
title_full Quiver Varieties and Branching
title_fullStr Quiver Varieties and Branching
title_full_unstemmed Quiver Varieties and Branching
title_sort quiver varieties and branching
author Nakajima, H.
author_facet Nakajima, H.
publishDate 2009
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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).
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149260
citation_txt Quiver Varieties and Branching / H. Nakajima // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ.
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first_indexed 2025-12-07T15:21:08Z
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