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15 September 2004 Matsuki correspondence for the affine Grassmannian
David Nadler
Duke Math. J. 124(3): 421-457 (15 September 2004). DOI: 10.1215/S0012-7094-04-12431-5

Abstract

Let $\mathcal{K}$=ℂ((t)) be the field of formal Laurent series, and let $\mathcal{O}$=ℂ[[t]] be the ring of formal power series. In this paper we present a version of the Matsuki correspondence for the affine Grassmannian Gr=G($\mathcal{K}$)/G($\mathcal{O}$) of a connected reductive complex algebraic group G. Our main statement is an anti-isomorphism between the orbit posets of two subgroups of G($\mathcal{K}$) acting on Gr. The first subgroup is the polynomial loop group LG of a real form G of G; the second is the loop group K($\mathcal{K}$) of the complexification K of a maximal compact subgroup Kc of G. The orbit poset itself turns out to be simple to describe.

Citation

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David Nadler. "Matsuki correspondence for the affine Grassmannian." Duke Math. J. 124 (3) 421 - 457, 15 September 2004. https://doi.org/10.1215/S0012-7094-04-12431-5

Information

Published: 15 September 2004
First available in Project Euclid: 31 August 2004

zbMATH: 1114.22012
MathSciNet: MR2084612
Digital Object Identifier: 10.1215/S0012-7094-04-12431-5

Subjects:
Primary: 22E67

Rights: Copyright © 2004 Duke University Press

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Vol.124 • No. 3 • 15 September 2004
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