Author

Waldeck Schutzer

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Preprint Sep 2026

Atomic Decompositions of Lie Characters and the Dominant Weight Poset

Let $\mathfrak{g}$ be a complex semisimple Lie algebra and, for a dominant integral weight $\lambda$, let $\Theta_\lambda$ be the multiplicity-free sum of the weights of the irreducible module $V(\lambda)$. The $\Theta_\mu$ form a $\mathbb{Z}$-basis of the $W$-invariants, so there are unique integers $a(\mu,\lambda)$,...

Felipe de Mattos Chafik Hindi, Waldeck Schutzer · 0 citations

Preprint Sep 2026

A classification of group gradings on incidence algebras over commutative rings

Let $R$ be a commutative ring with 1, $P$ a locally finite partially ordered set, and $G$ a group. We derive necessary and sufficient conditions for an $R$-algebra isomorphism between the incidence algebra $I(P,R)$ and the group algebra $RG$. Then, for an indecomposable ring $R$, a finite poset $P$ and an arbitrary gro...

Felipe de Mattos Chafik Hindi, Waldeck Schutzer · 0 citations