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On Certain Multiple Flag Varieties

Student: Marfa Krasnoselskaya

Supervisor: Evgeny Smirnov

Faculty: Faculty of Mathematics

Educational Programme: Joint Bachelor's Programme with the Centre for Teaching Excellence (Bachelor)

Final Grade: 9

Year of Graduation: 2021

We compute the number of orbits $P(k, l, n)$ of the group of upper-triangular matrices $B\subset\GL(n)$ acting on the direct product of two Grassmannians $\Gr(k, n)\times\Gr(k, n)$. We get an explicit formula for $1\le k < n$ and $l = 1$. We also state conjectures the number of orbits for the case $1 \le k, l < n$.

Full text (added May 28, 2021)

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