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DEGENERATE SCHUBERT VARIETIES IN TYPE A

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Abstract

We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated with a rectangular element is indeed a Schubert variety in a partial ag variety of the same type with larger rank. Moreover, the degenerate Demazure module associated with a rectangular element is isomorphic to the Demazure module for this particular Schubert variety of larger rank. This generalises previous results by Cerulli Irelli, Lanini and Littelmann for the PBW degenerate ag variety in [CLL].

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce, Italy

    ROCCO CHIRIVÌ

  2. Mathematisches Institut Universität zu Köln, 50931, Cologne, Germany

    XIN FANG

  3. Lehrstuhl für Algebra und Darstellungstheorie, RWTH Aachen University, 52056, Aachen, Germany

    GHISLAIN FOURIER

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  1. ROCCO CHIRIVÌ
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  2. XIN FANG
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  3. GHISLAIN FOURIER
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Correspondence to ROCCO CHIRIVÌ.

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CHIRIVÌ, R., FANG, X. & FOURIER, G. DEGENERATE SCHUBERT VARIETIES IN TYPE A. Transformation Groups 26, 1189–1215 (2021). https://doi.org/10.1007/s00031-020-09558-4

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