Equivalence classes of \(\mathrm{GL}(p, \mathbb{C})\times\mathrm{GL}(q,\mathbb{C})\) orbits in the flag variety of \(\mathfrak{gl}(p + q, \mathbb{C})\) (Q520434)
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scientific article; zbMATH DE number 6699709
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivalence classes of \(\mathrm{GL}(p, \mathbb{C})\times\mathrm{GL}(q,\mathbb{C})\) orbits in the flag variety of \(\mathfrak{gl}(p + q, \mathbb{C})\) |
scientific article; zbMATH DE number 6699709 |
Statements
Equivalence classes of \(\mathrm{GL}(p, \mathbb{C})\times\mathrm{GL}(q,\mathbb{C})\) orbits in the flag variety of \(\mathfrak{gl}(p + q, \mathbb{C})\) (English)
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3 April 2017
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The finite set of orbits of the subgroup \(\mathrm{GL}(p,\mathbb C) \times \mathrm{GL}(q,\mathbb C)\) on the flag variety of the group \(\mathrm{GL}(p+q,\mathbb C)\) is investigated. The authors prefer to use a combinatorial approach (which is based on the notion of clan) to parameterize such orbits. A combinatorial algorithmic description, amenable for computer computation, for nilpotent \(\mathrm{GL}(p,\mathbb C) \times \mathrm{GL}(q,\mathbb C)\)-orbits is presented.
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nilpotent orbits
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flag variety
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Young tableaux
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0.7994433045387268
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0.7994433045387268
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0.7763643860816956
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0.7716590762138367
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