Abstract
We give small deformations of a left-invariant complex structure on each simply connected semisimple compact Lie group of even dimension which are not biholomorphic to any left-invariant (right-invariant) complex structure by using the Kuranishi space. On such deformed complex manifolds, we prove the Borel–Weil–Bott type theorem, and we compute the cohomology of holomorphic tangent bundles.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: JP20K03592
Award Identifier / Grant number: JP19H01787
Award Identifier / Grant number: JP21K03248
Funding statement: The first author is supported by JSPS KAKENHI Grant Number JP20K03592. The second author is supported by JSPS KAKENHI Grant Numbers JP19H01787, JP21K03248.
Acknowledgements
We are grateful to the anonymous referee for the invaluable comments and useful suggestions on improving the text.
Communicated by: Shigeharu Takayama
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