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Mathematics > Representation Theory

arXiv:1808.01594 (math)
[Submitted on 5 Aug 2018 (v1), last revised 9 Feb 2019 (this version, v3)]

Title:Degenerate Schubert Varieties in Type A

Authors:Rocco Chirivi', Xin Fang, Ghislain Fourier
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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 to a rectangular element is indeed a Schubert variety in a partial flag variety of the same type with larger rank. Moreover, the degenerate Demazure module associated to a rectangular element is isomorphic to the Demazure module for this particular Schubert variety of larger rank. This generalizes previous results by Cerulli Irelli, Lanini and Littelmann for the PBW degenerate flag variety.
Comments: minor improvements; 28 pages, 6 figures
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG); Combinatorics (math.CO)
MSC classes: 17B10, 16S30, 14M15, 06A07
Cite as: arXiv:1808.01594 [math.RT]
  (or arXiv:1808.01594v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1808.01594

Submission history

From: Rocco Chirivì [view email]
[v1] Sun, 5 Aug 2018 10:19:02 UTC (24 KB)
[v2] Fri, 7 Sep 2018 10:58:09 UTC (26 KB)
[v3] Sat, 9 Feb 2019 22:27:27 UTC (26 KB)
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