Symplectic restriction varieties and geometric branching rules II

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• 作者：Izzet Coskun ^{coskun@math.uic.edu" class="auth_mail}
• 关键词：Flag varieties ; Homogeneous spaces ; Restriction problem
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：July 2014
• 年：2014
• 卷：125
• 期：Complete
• 页码：47-97
• 全文大小：561 K

文摘

In this paper, we introduce combinatorially defined subvarieties of symplectic flag varieties called symplectic restriction varieties  . We study their geometric properties and compute their cohomology classes. In particular, we give a positive, combinatorial, geometric branching rule for computing the map in cohomology induced by the inclusion of the symplectic partial flag variety SF(k₁,…,k_h;n)$\mathit{SF}(k_1,\dots ,k_h;n)$ in the partial flag variety F(k₁,…,k_h;n)$F(k_1,\dots ,k_h;n)$. These rules have many applications in algebraic geometry, combinatorics, symplectic geometry and representation theory.