A binary operation on irreducible components of Lusztig's nilpotent varieties {I}: definition and properties

TL;DR

This paper introduces a new binary operation on irreducible components of Lusztig's nilpotent varieties, analyzing its algebraic properties and methods for constructing rigid components.

Contribution

It defines and investigates a novel binary operation on irreducible components of Lusztig's nilpotent varieties, including properties and construction techniques.

Findings

The operation's commutativity, cancellativity, and associativity are studied.

Methods for inductively constructing rigid irreducible components are discussed.

The operation provides new insights into the structure of Lusztig's nilpotent varieties.

Abstract

We define a binary operation on the set of irreducible components of Lusztig's nilpotent varieties of a quiver. We study commutativity, cancellativity and associativity of this operation. We focus on rigid irreducible components and discuss inductive ways to construct them.