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Schubert polynomials and the Littlewood-Richardson rule

✍ Scribed by Alain Lascoux; Marcel-Paul Schützenberger

Publisher
Springer
Year
1985
Tongue
English
Weight
648 KB
Volume
10
Category
Article
ISSN
0377-9017

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✦ Synopsis

The decomposition of a product of two irreducible representations of a linear group GI(N, C) is explicitly given by the Littlewood-Richardson rule, which amounts to finding how many Young tableaux satisfy certain conditions. We obtain more general multiplicities by generating 'vexillary' permutations and by using partially symmetrical polynomials (Schubert polynomials).

📜 SIMILAR VOLUMES

On the Littlewood–Richardson polynomials
On the Littlewood–Richardson polynomials
✍ Harm Derksen; Jerzy Weyman 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 95 KB

We prove the equivalence of several descriptions of generators of rings of semiinvariants of quivers, due to Domokos and Zubkov, Schofield and van den Bergh, and our earlier work. We also show that the dimensions of semi-invariants of weights nσ depend polynomially on n.