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Irreducibility, Smoothness, and Connectivity of Realization Spaces of Matroids and Hyperplane Arrangements
Emiliano Liwski, Fatemeh Mohammadi
We study the realization spaces of matroids and hyperplane arrangements. First, we define the notion of naive dimension for the realization space of matroids and compare it with th…
Representations of Yokonuma--Hecke algebras
Emiliano Liwski, Martín Mereb
The Iwahori--Hecke and Yokonuma--Hecke algebras have played crucial roles in algebraic combinatorics and the representation theory of finite groups. In this work, we use classical…
Solvable and Nilpotent Matroids: Realizability and Irreducible Decomposition of Their Associated Varieties
Emiliano Liwski, Fatemeh Mohammadi
We introduce the families of solvable and nilpotent matroids, examining their realization spaces, closures, and associated matroid and circuit varieties. We study their realizabili…
Paving Matroids: Defining Equations and Associated Varieties
Emiliano Liwski, Fatemeh Mohammadi
We study paving matroids, their realization spaces, and their closures, along with matroid varieties and circuit varieties. Within this context, we introduce three distinct methods…