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Representation theory and ADHM-construction on quaternion symmetric spaces


Author: Yasuyuki Nagatomo
Journal: Trans. Amer. Math. Soc. 353 (2001), 4333-4355
MSC (1991): Primary 53C07, 32M10, 53C26
DOI: https://doi.org/10.1090/S0002-9947-01-02829-X
Published electronically: June 14, 2001
MathSciNet review: 1851173
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Abstract:

We determine all irreducible homogeneous bundles with anti-self-dual canonical connections on compact quaternion symmetric spaces. To deform the canonical connections, we give a relation between the representation theory and the theory of monads on the twistor space. The moduli spaces are described via the Bott-Borel-Weil Thereom. The Horrocks bundle is also generalized to higher-dimensional projective spaces.


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Additional Information

Yasuyuki Nagatomo
Affiliation: Department of Mathematics, Sophia University, Kioicho, Tokyo 102, Japan
Address at time of publication: Faculty of Mathematics, Kyushu University, Ropponmatsu, Fukuoka 810-8560, Japan
Email: nagatomo@math.kyushu-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-01-02829-X
Keywords: ADHM-construction, quaternion symmetric space, monad, moduli
Received by editor(s): October 25, 1996
Received by editor(s) in revised form: September 7, 2000
Published electronically: June 14, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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