Symplectomorphism group of \(T^\ast (G_{\mathbb{C}} / B)\) and the braid group. I: A homotopy equivalence for \(G_{\mathbb{C}} = \mathrm{SL}_3 (\mathbb{C})\)

DOI10.4310/JSG.2019.V17.N2.A2zbMATH Open1473.57079arXiv1412.0511OpenAlexW2964697011MaRDI QIDQ2318834

Author name not available (Why is that?)

Publication date: 16 August 2019

Published in: (Search for Journal in Brave)

Abstract: For a semisimple Lie group

G_{m} a t h b b C

over

m a t h b b C

, we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation to the braid group. We prove a homotopy equivalence between the two groups in the case of

G_{m} a t h b b C = S L_{3} (m a t h b b C)

, under the

S U (3)

-equivariancy condition on symplectomorphisms.

Full work available at URL: https://arxiv.org/abs/1412.0511

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