arXiv subjects

Sebastiano Argenti

Publications and source records attributed to Sebastiano Argenti.

3 recordsLinked to original sources

arXiv2026

Unbalanced distance-biregular graphs with girth deficiency two

Let $Γ=(V,E)$ be a distance-biregular graph with even diameter $d$ and girth $2d-2$. On the edge-set $E$ we define relations that form an association scheme; this is done by considering the linear span of the corresponding adjacency matrices, and, by means of intersection diagrams, we prove that this is an algebra. Furthermore, we describe all the irreducible representations of this algebra, and, by considering the multiplicities of the 2-dimensional ones, we show that there are no such distance-biregular graphs with $28\le d\le 46$ and $d\ge 52$.

math.CO↗

arXiv2025

Cocharacters of generalized polynomial identities

In this paper we extend the cocharacter theory to generalized identities of $W$-algebras. We prove that the Hilbert series of the relatively free $W$-algebra admits an expansion in terms of Schur functions whose coefficients coincide with generalized cocharacter multiplicities. Moreover, we prove analogues of the Hook and Strip theorems for $W$-algebras and we derive growth bounds for generalized codimension and colenght sequences. Finally, we establish that every variety $\mathcal{V}$ of $W$-algebras is generated by the Grassmann envelope of a finitely generated $W$-superalgebra, and if $\mathcal{V}$ satisfies a generalized Capelli set, then it is generated by a finitely generated $W$-algebra.

math.RA↗

arXiv2025

Group gradings on exceptional simple Lie superalgebras

We classify up to isomorphism the gradings by arbitrary groups on the exceptional classical simple Lie superalgebras $G(3)$, $F(4)$ and $D(2,1;α)$ over an algebraically closed field of characteristic $0$. To achieve this, we apply the recent method developed by A. Elduque and M. Kochetov to the known classification of fine gradings up to equivalence on the same superalgebras, which was obtained by C. Draper et al. in 2011. We also classify gradings on the simple Lie superalgebra $A(1,1)$, whose automorphism group is different from the other members of the $A$ series.

math.RA↗