Classic and Mirabolic Robinson–Schensted–Knuth Correspondence for Partial Flags

Rosso, Daniele

doi:10.4153/cjm-2011-071-7

Cited by 10 publications

(15 citation statements)

References 13 publications

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“…Specifically Travkin [Tra09] and Rosso [Ros12] describe geometric correspondences ("mirabolic RSK correspondences") relating triple flag varieties and enhanced nilpotent varieties.…”

Section: Whose Fibers Have At Most Two Elements (B)mentioning

confidence: 99%

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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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“…Specifically Travkin [Tra09] and Rosso [Ros12] describe geometric correspondences ("mirabolic RSK correspondences") relating triple flag varieties and enhanced nilpotent varieties.…”

Section: Whose Fibers Have At Most Two Elements (B)mentioning

confidence: 99%

“…We also mention that there are some related works on triple flag varieties, which are special cases of the double flag varieties of symmetric pairs as seen from Example 1.2 (b). Specifically Travkin [Tra09] and Rosso [Ros12] describe geometric correspondences ("mirabolic RSK correspondences") relating triple flag varieties and enhanced nilpotent varieties.…”

mentioning

confidence: 99%

On the exotic Grassmannian and its nilpotent variety

Fresse¹,

Nishiyama²

2016

Represent. Theory

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“…We denote by T the set of pairs of inverted Young tableaux (P, Q) of the same shape. (See [23] for a similar nonstandard convention. The appendix of [8] also discusses closely related variants of RSK.)…”

Section: Rsk For Multisegmentsmentioning

confidence: 99%

“…Both the Zelevinsky classification and the RSK correspondence admit geometric interpretations (starting with [31,32] for the former, [23,26,28] for the latter). However, we are not aware of a geometric interpretation of the abovementioned partial order defined through RSK.…”

Section: Introductionmentioning

confidence: 99%

Robinson–Schensted–Knuth correspondence in the representation theory of the general linear group over a non-archimedean local field

Gurevich

Lapid

2021

Represent. Theory

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We construct new “standard modules” for the representations of general linear groups over a local non-archimedean field. The construction uses a modified Robinson–Schensted–Knuth correspondence for Zelevinsky’s multisegments. Typically, the new class categorifies the basis of Doubilet, Rota, and Stein (DRS) for matrix polynomial rings, indexed by bitableaux. Hence, our main result provides a link between the dual canonical basis (coming from quantum groups) and the DRS basis.

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“…Also, in [Kat09], Kato considered an "exotic" nilpotent cone and give the Deligne-Langlands theory for those exotic nilpotent orbits. There are many related works based on algebraic geometry, combinatorial theory, and theory of character sheaves ( [Tra09], [FGT09], [HT12], [FN16], [Ros12]).…”

Section: Introductionmentioning

confidence: 99%