Chromatic symmetric functions via the group algebra of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msub></mml:math>

We prove some Schur positivity results for the chromatic symmetric function X G of a (hyper)graph G, using connections to group algebra group. The first such connection works (hyper)forests F: we describe coefficients F in terms eigenvalues product Hermitian idempotents algebra, one factor each edge (a more general formula similar shape holds all chordal graphs). Our main application this technique is conjecture Taylor on certain , which implies formal laws associated various combinatorial generating functions. also introduce pointed G,v rooted graph (G,v). that if and H,w are positive generalized basis Strahov, then wedge sum (G,v) (H,w) positive.