Invariant Einstein metrics on $\mathrm{SU}(n)$ and complex Stiefel manifolds

2020 ◽  
Vol 72 (2) ◽  
pp. 161-210 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Yusuke Sakane ◽  
Marina Statha
Keyword(s):  
Einstein Metrics ◽  
Stiefel Manifolds

Discrete Geodesic Flows on Stiefel Manifolds

2020 ◽  
Vol 310 (1) ◽  
pp. 163-174
Author(s):  
Božidar Jovanović ◽  
Yuri N. Fedorov
Keyword(s):  
Geodesic Flows ◽  
Stiefel Manifolds

scholarly journals Whitehead products in the complex Stiefel manifolds

1983 ◽  
Vol 26 (2) ◽  
pp. 241-251 ◽  
Author(s):  
Yasukuni Furukawa
Keyword(s):  
Stiefel Manifold ◽  
Isotropy Group ◽  
Homotopy Groups ◽  
Stiefel Manifolds

The complex Stiefel manifoldWn,k, wheren≦k≦1, is a space whose points arek-frames inCn. By using the formula of McCarty [4], we will make the calculations of the Whitehead products in the groups π*(Wn,k). The case of real and quaternionic will be treated by Nomura and Furukawa [7]. The product [[η],j1l] appears as generator of the isotropy group of the identity map of Stiefel manifolds. In this note we use freely the results of the 2-components of the homotopy groups of real and complex Stiefel manifolds such as Paechter [8], Hoo-Mahowald [1], Nomura [5], Sigrist [9] and Nomura-Furukawa [6].

On Borel–de Siebenthal Representations

2018 ◽  
Vol 2019 (15) ◽  
pp. 4845-4858
Author(s):  
Jing-Song Huang ◽  
Yongzhi Luan ◽  
Binyong Sun
Keyword(s):  
Analytic Continuation ◽  
Lie Groups ◽  
Discrete Series ◽  
Root Systems ◽  
Stiefel Manifolds ◽  
Simple Lie Groups

AbstractHolomorphic representations are lowest weight representations for simple Lie groups of Hermitian type and have been studied extensively. Inspired by the work of Kobayashi on discrete series for indefinite Stiefel manifolds, Gross–Wallach on quaternonic discrete series and their analytic continuation, and Ørsted–Wolf on Borel–de Siebenthal discrete series, we define and study Borel–de Siebenthal representations (also called quasi-holomorphic representations) associated with Borel–de Siebenthal root systems for simple Lie groups of non-Hermitian type.

scholarly journals On vector bundles for a Morse decomposition of $L\mathbb{C}\mathrm{P}^n$

2017 ◽  
Vol 121 (2) ◽  
pp. 186
Author(s):  
Iver Ottosen
Keyword(s):  
Loop Space ◽  
Vector Bundles ◽  
Morse Decomposition ◽  
Energy Integral ◽  
Chern Classes ◽  
Free Loop Space ◽  
Stiefel Manifolds ◽  
Mod P

We give a description of the negative bundles for the energy integral on the free loop space $L\mathbb{C}\mathrm{P}^n$ in terms of circle vector bundles over projective Stiefel manifolds. We compute the mod $p$ Chern classes of the associated homotopy orbit bundles.

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