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Combinatorial Laplacian of the matching complex. (English) Zbl 0985.05052
Electron. J. Comb. 9, No. 1, Research paper R17, 11 p. (2002); printed version J. Comb. 9, No. 1 (2002).
Summary: A striking result of Bouc gives the decomposition of the representation of the symmetric group on the homology of the matching complex into irreducibles that are self-conjugate. We show how the combinatorial Laplacian can be used to give an elegant proof of this result. We also show that the spectrum of the Laplacian is integral.

MSC:
05E10 Combinatorial aspects of representation theory
05E25 Group actions on posets, etc. (MSC2000)
05E05 Symmetric functions and generalizations
20C30 Representations of finite symmetric groups
55U10 Simplicial sets and complexes in algebraic topology
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