Multiple Flag Varieties of Finite Type

Magyar, Péter; Weyman, Jerzy; Zelevinsky, Andrei

doi:10.1006/aima.1998.1776

Cited by 89 publications

(141 citation statements)

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“…Triple flag varieties of the form G/P 1 × G/P 2 × G/P 3 consist of infinitely many G-orbits in general. Triple flag varieties with finite number of G-orbits are classified in [MWZ99], [MWZ00] in the classical cases (see also [Mat13]). …”

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confidence: 99%

On the exotic Grassmannian and its nilpotent variety

Fresse¹,

Nishiyama²

2016

Represent. Theory

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Abstract. Given a decomposition of a vector space V = V 1 ⊕ V 2 , the direct product X of the projective space P(V 1 ) with a Grassmann variety Gr k (V ) can be viewed as a double flag variety for the symmetric pair (G, K) = (GL(V ), GL(V 1 ) × GL(V 2 )). Relying on the conormal variety for the action of K on X, we show a geometric correspondence between the K-orbits of X and the K-orbits of some appropriate exotic nilpotent cone. We also give a combinatorial interpretation of this correspondence in some special cases. Our construction is inspired by a classical result of Steinberg (1976) and by the recent work of Henderson and Trapa (2012) for the symmetric pair (GL(V ), Sp(V )).

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confidence: 99%

On the exotic Grassmannian and its nilpotent variety

Fresse¹,

Nishiyama²

2016

Represent. Theory

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“…Unfortunately it is not true that the generic subspace has the maximal dimension for general Lie group actions, even those that are algebraic, for an explicit counterexample see [4]. Thus we define…”

Section: Preliminaries and Main Resultsmentioning

confidence: 99%

Moduli space of symmetric connections

Dubrovskiy¹

2005

J Math Sci

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“…It comes equipped with a Kazhdan-Lusztig basis numbered by the finite set RB N of GL(V )-orbits in Fl(V ) × Fl(V ) × V , described in [18] (see also [15,16]). Thus we can define a partition of RB N into bimodule KL cells.…”

Section: 3mentioning

confidence: 99%

Mirabolic Robinson–Shensted–Knuth correspondence

Travkin

2009

Sel. math., New ser.

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Abstract. The set of orbits of GL(V ) in F l(V ) × F l(V ) × V is finite, and is parametrized by the set of certain decorated permutations in a work of Solomon. We describe a Mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of standard Young tableaux, and an extra partition. It gives rise to a partition of the set of orbits into combinatorial cells. We prove that the same partition is given by the type of a general conormal vector to an orbit. We conjecture that the same partition is given by the bimodule Kazhdan-Lusztig cells in the bimodule over the Iwahori-Hecke algebra of GL(V ) arising from F l(V ) × F l(V ) × V . We also give conjectural applications to the classification of unipotent mirabolic character sheaves on GL(V ) × V .

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Multiple Flag Varieties of Finite Type

Abstract: We classify all products of flag varieties with finitely many orbits under the diagonal action of the general linear group. We also classify the orbits in each case and construct explicit representatives. Academic Press

Cited by 89 publications

References 8 publications

On the exotic Grassmannian and its nilpotent variety

On the exotic Grassmannian and its nilpotent variety

Moduli space of symmetric connections

Mirabolic Robinson–Shensted–Knuth correspondence

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