Ulrich Schur bundles on flag varieties

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• 作者：Izzet Coskun^a ; ^{coskun@math.uic.edu} ; Laura Costa^b ; ^costa@ub.edu ; Jack Huizenga^c ; ^{huizenga@psu.edu} ; Rosa Maria Miró ; -Roig^b ; ^miro@ub.edu ; Matthew Woolf^a ; ^{woolf@math.uic.edu}
• 关键词：primary ; 14M15 ; secondary ; 14J60 ; 13C14 ; 13D02 ; 14F05
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：474
• 期：Complete
• 页码：49-96
• 全文大小：878 K
• 卷排序：474

文摘

In this paper, we study equivariant vector bundles on partial flag varieties arising from Schur functors. We show that a partial flag variety with three or more steps does not admit an Ulrich bundle of this form with respect to the minimal ample class. We classify Ulrich bundles of this form on two-step flag varieties F(1,n−1;n)F(1,n−1;n), F(2,n−1;n)F(2,n−1;n), F(2,n−2;n)F(2,n−2;n), F(k,k+1;n)F(k,k+1;n) and F(k,k+2;n)F(k,k+2;n). We give a conjectural description of the two-step flag varieties which admit such Ulrich bundles.