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Double Flag Varieties for Symmetric Pairs and Representations of Quivers

Hold Date
2021-05-06 17:30〜2021-05-06 18:00
Object person
Hiroki Homma (Kyushu University)

Abstract : For a reductive group G and a symmetric subgroup K, the direct product G/P × K/Q of partial flag varieties G/P and K/Q is called a double flag variety for a symmetric pair (G, K). Here, the diagonal action of K on G/P×K/Q is a vital object applied to branching rules of representations.
In particular, two problems are as follows:
(1)What are the pairs G, K, P, and Q such that there are only finitely many K-orbits on G/P×K/Q?
(2)Can we describe the K-orbits on G/P × K/Q when there are only finitely many K-orbits? Therefore, we classified P and Q such that the number of K-orbits is finite for G=GL_{m+n} and K=GL_{m}×GL_{n}, and also described their orbit decomposition.
We solved the problem by providing a correspondence between the K-orbits and the quiver representations. We will talk about the above in the seminar.

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