Invariants of the Cox rings of low-complexity double flag varieties for classical groups

Ponomareva, E.

doi:10.1090/mosc/244

Invariants of the Cox rings of low-complexity double flag varieties for classical groups
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by E. V. Ponomareva
Translated by: V. E. Nazaikinskii

Trans. Moscow Math. Soc. 2015, 71-133

DOI: https://doi.org/10.1090/mosc/244

Published electronically: November 17, 2015

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Abstract:

We find the algebras of unipotent invariants of Cox rings for all double flag varieties of complexity $0$ and $1$ for the classical groups; namely, we obtain presentations of these algebras. It is well known that such an algebra is simple in the case of complexity $0$. We show that, in the case of complexity $1$, the algebra in question is either a free algebra or a hypersurface. Knowing the structure of this algebra permits one to effectively decompose tensor products of irreducible representations into direct sums of irreducible representations.

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