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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

   
 

 

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


Author: E. V. Ponomareva
Translated by: V. E. Nazaikinskii
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 76 (2015), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2015, 71-133
MSC (2010): Primary 14L35; Secondary 14M17
DOI: https://doi.org/10.1090/mosc/244
Published electronically: November 17, 2015
MathSciNet review: 3467261
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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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Additional Information

E. V. Ponomareva
Affiliation: Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Email: lizaveta@yandex.ru

DOI: https://doi.org/10.1090/mosc/244
Keywords: Double flag variety, Cox ring, complexity, linear representation, tensor product of representations, branching problem.
Published electronically: November 17, 2015
Article copyright: © Copyright 2015 E. V. Ponomareva