Codes, transforms and the spectrum of the symmetric group

Paul Henry Edelman and Dennis E. White

Vol. 143 (1990), No. 1, 47–67

DOI: 10.2140/pjm.1990.143.47

Abstract

Let G_n be the graph of permutations with edges drawn between permutations differing by an adjacent transposition. Using the Kazhdan-Lusztig representations of S_n and combinatorial arguments, we show that integers frequently occur in the spectrum of G_n. That 0 and −1 are among the integers which arise has application to finite Radon transforms and to existence of perfect 1-codes on G_n.

Mathematical Subject Classification 2000

Primary: 20C30

Secondary: 05C25, 05C50, 94B60

Milestones

Received: 23 May 1988

Revised: 19 September 1988

Published: 1 May 1990