Tensor invariants, saturation problems, and Dynkin automorphisms

Jiuzu Hong Linhui Shen

Representation Theory mathscidoc:1912.43245

Advances in Mathematics, 285, 629-657, 2015.11
Let G be a connected almost simple algebraic group with a Dynkin automorphism . Let G be the connected almost simple algebraic group associated with G and . We prove that the dimension of the tensor invariant space of G is equal to the trace of on the corresponding tensor invariant space of G. We prove that if G has the saturation property then so does G . As a consequence, we show that the spin group Spin (2 n+ 1) has saturation factor 2, which strengthens the results of BelkaleKumar [1] and Sam [28] in the case of type B n.
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@inproceedings{jiuzu2015tensor,
  title={Tensor invariants, saturation problems, and Dynkin automorphisms},
  author={Jiuzu Hong, and Linhui Shen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113157456736805},
  booktitle={Advances in Mathematics},
  volume={285},
  pages={629-657},
  year={2015},
}
Jiuzu Hong, and Linhui Shen. Tensor invariants, saturation problems, and Dynkin automorphisms. 2015. Vol. 285. In Advances in Mathematics. pp.629-657. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113157456736805.
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