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Quiver Varieties and Branching

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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Main Author: Nakajima, H.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/149260
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spelling irk-123456789-1492602019-02-20T01:26:37Z Quiver Varieties and Branching Nakajima, H. 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). 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149260 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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).
format Article
author Nakajima, H.
spellingShingle Nakajima, H.
Quiver Varieties and Branching
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Nakajima, H.
author_sort Nakajima, H.
title Quiver Varieties and Branching
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
publisher Інститут математики НАН України
publishDate 2009
url http://dspace.nbuv.gov.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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT nakajimah quivervarietiesandbranching
first_indexed 2023-05-20T17:32:35Z
last_indexed 2023-05-20T17:32:35Z
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