Double Flag Varieties and Representations of Quivers

TL;DR

This paper classifies double flag varieties with finitely many K-orbits for a specific symmetric pair and establishes a correspondence between these orbits and quiver representations, advancing understanding in geometric representation theory.

Contribution

It provides a classification of finite K-orbits in double flag varieties for GL_{m+n} and relates them to quiver representations, offering new insights into orbit structure.

Findings

Finite classification of K-orbits in double flag varieties.

Explicit correspondence between K-orbits and quiver representations.

Descriptions of K-orbit structures when finite.

Abstract

We gave a classification of P and Q with a finite number of K-orbits of a double flag variety G/P*K/Q for a symmetric pair (G, K) when G=GL_{m+n} and K=GL_{m}*GL_{n}, and a description of K-orbits when the number of K-orbits of G/P*K/Q is finite. We solved the problem by providing a correspondence between the K-orbits and the quiver representations.