Symmetric quiver settings with a regular ring of invariants

A Quiver Construction of Symmetric Crystals

In the papers [EK1], [EK2] and [EK3] with Masaki Kashiwara, the author introduced the notion of symmetric crystals and presented the Lascoux-Leclerc-ThibonAriki type conjectures for the affine Hecke algebras of type B. Namely, we conjectured that certain composition multiplicities and branching rules for the affine Hecke algebras of type B are described by using the lower global basis of symmet...

Quiver mutation and combinatorial DT-invariants

A quiver is an oriented graph. Quiver mutation is an elementary operation on quivers. It appeared in physics in Seiberg duality in the nineties and in mathematics in the definition of cluster algebras by Fomin-Zelevinsky in 2002. We show how, for large classes of quivers Q, using quiver mutation and quantum dilogarithms, one can construct the combinatorial DT-invariant, a formal power series in...

The Cohomology Ring of Truncated Quiver Algebras

In this paper we determine the ring structure of the Hochschild cohomology of truncated quiver algebras with the Yoneda product. On the one hand Locateli described the cohomology groups in terms of classes of pairs of paths using minimal resolutions. On the other hand, the Yoneda product has a nice description on the bar resolution as the usual cup product. Our first main result is the explicit...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

Hirzebruch invariants of symmetric products

These notes are an expanded version of the talk given by the first author at the conference “Topology of Algebraic Varieties”, organized in honor of Anatoly Libgober’s 60-th anniversary. We provide here a very elementary proof of a generating series formula for the Hodge polynomials (with coefficients) of symmetric products of quasi-projective varieties. A more general result was recently obtai...