Quiver varieties and path realizations arising from adjoint crystals of type A(1) n

Seok Jin Kang; Euiyong Park

doi:10.1090/S0002-9947-2011-05246-3

Quiver varieties and path realizations arising from adjoint crystals of type A⁽¹⁾ _n

Seok Jin Kang, Euiyong Park

Department of Mathematics

Seoul National University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let B(Λ0) be the level 1 highest weight crystal of the quantum affine algebra Uq(A⁽¹⁾ _n). We construct an explicit crystal isomorphism between the geometric realization B(Λ0) of B(Λ0) via quiver varieties and the path realization Pad(Λ0) of B(Λ0) arising from the adjoint crystal Bad.

Original language	English
Pages (from-to)	5341-5366
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	363
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9947-2011-05246-3
State	Published - Oct 2011

Keywords

Adjoint crystal
Crystal graph
Kac-moody algebra
Path realization
Quiver variety

Access to Document

10.1090/S0002-9947-2011-05246-3

Cite this

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title = "Quiver varieties and path realizations arising from adjoint crystals of type A(1) n",

abstract = "Let B(Λ0) be the level 1 highest weight crystal of the quantum affine algebra Uq(A(1) n). We construct an explicit crystal isomorphism between the geometric realization B(Λ0) of B(Λ0) via quiver varieties and the path realization Pad(Λ0) of B(Λ0) arising from the adjoint crystal Bad.",

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KW - Kac-moody algebra

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