Osaka Journal of Mathematics

A combinatorial decomposition of higher level Fock spaces

Nicolas Jacon and Cédric Lecouvey

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We give a simple characterization of the highest weight vertices in the crystal graph of the level $l$ Fock spaces. This characterization is based on the notion of totally periodic symbols viewed as affine analogues of reverse lattice words classically used in the decomposition of tensor products of fundamental $\mathfrak{sl}_{n}$-modules. This yields a combinatorial decomposition of the Fock spaces in their irreducible components and the branching law for the restriction of the irreducible highest weight $\mathfrak{sl}_{\infty}$-modules to $\widehat{\mathfrak{sl}}_{e}$.

Article information

Osaka J. Math., Volume 50, Number 4 (2013), 897-920.

First available in Project Euclid: 9 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 20G42: Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50] 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]


Jacon, Nicolas; Lecouvey, Cédric. A combinatorial decomposition of higher level Fock spaces. Osaka J. Math. 50 (2013), no. 4, 897--920.

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