Lefschetz decompositions for eigenforms on a Kähler manifold

Abstract

We show that the eigenspaces of the Laplacian Δ k \Delta _k on k k -forms on a compact Kähler manifold carry Hodge and Lefschetz decompositions. Among other consequences, we show that the positive part of the spectrum of Δ k \Delta _k lies in the spectrum of Δ k + 1 \Delta _{k+1} for k > dim ⁡ X k>\dim X .