This article is cited in 6 papers

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

E. V. Ponomareva

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

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.

Key words and phrases: Double flag variety, Cox ring, complexity, linear representation, tensor product of representations, branching problem.

UDC: 512.743.7

MSC: 14L35, 14M17

Received: 28.04.2014
Revised: 16.10.2014

 English version: Transactions of the Moscow Mathematical Society, 2015, 76:1, 71–133

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