On double Veronese embeddings in the Grassmannian G(1,N)
J. C. Sierra, L. Ugaglia
我们对P^n的所有嵌入进行分类，使得与Plücker的合成由P^n的二次曲面的线性系给出。
We classify all the embeddings of P^n in a Grassmannian of lines G(1,N) such that the composition with Plücker is given by a linear system of quadrics of P^n.
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In this note we describe the image of $\PP^2$ in $ Gr(2, \CC^{4})$ under a morphism given by a rank two vector bundle on $\PP^2$ with Chern classes $(2,2).$
On Triple Veronese Embeddings of $\PP_n$ in the Grassmannians
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Double Veronese cones with singularities
研究具有终端Gorenstein奇点的双重Veronese锥，确定节点数上限，分析自同构群结构，并建立有理性和无理性的判据。
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Using localization methods on the moduli space of stable quasimaps to Grassmannian, we give explicit formulas of $J$-function and double $J$-function of stable quasimaps for complete intersection in Grassmannian.
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Deformation rigidity of the double Cayley Grassmannian
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Stringy $E$-functions of Pfaffian-Grassmannian double mirrors
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Pursuing the double affine Grassmannian III: Convolution with affine Zastava
这是一系列论文中的第三篇（由arXiv：0711.2083，arXiv：0908.3390开始），描述了仿射Kac-Moody群的仿射格拉斯曼（也称为双仿射格拉斯曼）的一个几何模拟。目前的文件是致力于描述的卷积图的双仿射格拉斯曼和仿射Zastava的一个几何模拟。
Pursuing the double affine Grassmannian II: Convolution
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k-Double Schur functions and equivariant (co)homology of the affine Grassmannian
特殊线性群的仿射格拉斯曼环的环面等变同调环和上同调环的Schubert基由新的对称函数族k-双Schur函数和仿射双Schur函数实现.
We study the double Grothendieck polynomials of Kirillov--Naruse for the symplectic and odd orthogonal Grassmannians. These functions are explicitly written as sums of Pfaffian and are identified with the stable limits of the fundamental classes of Schubert varieties in the torus equivariant connective K-theory of these isotropic Grassmannians. We also provide a combinatorial description of the ring formally spanned by double Grothendieck polynomials.
Double transitivity of Galois Groups in Schubert Calculus of Grassmannians
研究了格拉斯曼算子上经典Schubert演算中伽罗瓦群的双传递性.我们证明了2-平面和3-平面上的格拉斯曼算子上的所有舒伯特问题都有双传递的伽罗瓦群，就像所有只涉及特殊舒伯特条件的舒伯特问题一样。利用这些结果给出了2-平面Grassmannian上的Schubert问题具有包含交错群的伽罗瓦群的新证明。我们还研究了Gr（4，8）上每个Schubert问题的伽罗瓦群，发现每个伽罗瓦群要么包含交错群，要么是非本原的置换群，因而不能是双传递的.这些非本原的例子表明，我们的结果是Schubert问题双传递性的最好的可能的一般结果。
We unify aspects of the equivariant geometry of type $D$ quiver representation varieties, double Grassmannians, and symmetric varieties $GL(a+b)/GL(a)\times GL(b)$; in particular we translate results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivariant $K$-theory between these three families. These results are all obtained from our generalization of a construction of Zelevinsky for type $A$ quivers to the type $D$ setting. More precisely, we give explicit embeddings with nice properties of homogeneous fiber bundles over type $D$ quiver repres…
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设X是有限维向量空间V中k-平面和l-平面的两个格拉斯曼簇的直积，B是V中完备旗的各向同性群。我们考虑X中的B-轨道，它类似于格拉斯曼空间中的Schubert胞腔。我们描述了这一组轨道组合和构造desingularizations关闭这些轨道，类似的博特-萨麦尔森desingularizations舒伯特品种。
We propose a conjectural construction of various slices for double affine Grassmannians as Coulomb branches of 3-dimensional N=4 supersymmetric affine quiver gauge theories. It generalizes the known construction for the usual affine Grassmannian, and makes sense for arbitrary symmetric Kac-Moody algebras.
Nets of conics containing a double line in $\mathrm{PG}(2,q)$, $q$ even
本文完成了偶数阶有限域射影平面上含双直线的二次曲线网的分类，得到18个等价类，其中9个基为空，并有助于部分对称张量的分类。
Pursuing the double affine Grassmannian I: transversal slices via instantons on A_k-singularities
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Equivariant $K$-homology of affine Grassmannian and $K$-theoretic double $k$-Schur functions
本文研究仿射格拉斯曼流形的环面等变 $K$-同调环，在 $A$ 型中引入 $K$-理论双重 $k$-Schur 函数作为 Schubert 基，并给出 $\mathrm{Gr}_{{SL}_n}$ 的等变 $K$-同调环的 Ginzburg-Peterson 型实现。
Proving the 6d a-theorem with the double affine Grassmannian
本文通过$E_8$的双重仿射Grassmannian的Hasse图描述6d $(1,0)$ SCFTs的Higgs branch RG流层级，并利用其偏序证明a定理，穷尽偶维超对称设定下的c定理。
Two dimensional versions of the affine Grassmannian and their geometric description
本文研究了二维仿射Grassmannian的几何描述，证明了在$G$为可解群时其可表示为ind-schemes，并通过向量包和平凡化数据给出了其几何解释。
We study the Littlewood-Richardson coefficients of double Grothendieck polynomials indexed by Grassmannian permutations. Geometrically, these are the structure constants of the equivariant $K$-theory ring of Grassmannians. Representing the double Grothendieck polynomials as partition functions of an integrable vertex model, we use its Yang-Baxter equation to derive a series of product rules for the former polynomials and their duals. The Littlewood-Richardson coefficients that arise can all be expressed in terms of puzzles without gashes, which generalize previous puzzles obtained by Knutson-T…
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