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On the combinatorics of rational representations of the group \(GL(n,{\mathbb{C}})\). (Russian. English summary) Zbl 0797.20034

Summary: A generalized Robinson-Schensted-Knuth correspondence is constructed associated with the decomposition of representations of \(GL(n,\mathbb{C})\) in mixed tensor spaces.

MSC:

20G05 Representation theory for linear algebraic groups
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
05E15 Combinatorial aspects of groups and algebras (MSC2010)
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