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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Affine Grassmannians for G_2
仿射 格拉斯曼代数 G_2
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2023/4/14
I will talk about affine Grassmannians for the exceptional group of type G_2. This group can be given as automorphisms of octonion algebras. I consider all maximal parahoric subgroups in G_2, and give...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Derived Grassmannians, derived Schur functors, and their applications
派生 格拉斯曼量 舒尔函子 应用
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2023/4/21
In this talk, we will revisit Grothendieck's theory of Grassmannians and flag schemes and the theory of Schur and Weyl module functors studied in $GL_n$-representation theory from theperspective of de...
A GIAMBELLI FORMULA FOR EVEN ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS GIAMBELLI FORMULA
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2015/12/17
Let X be an orthogonal Grassmannian parametrizing isotropic
subspaces in an even dimensional vector space equipped with a nondegenerate
symmetric form. We prove a Giambelli formula which expresses a...
A GIAMBELLI FORMULA FOR ISOTROPIC GRASSMANNIANS
ISOTROPIC GRASSMANNIANS GIAMBELLI FORMULA
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2015/12/17
Let X be a symplectic or odd orthogonal Grassmannian. We prove
a Giambelli formula which expresses an arbitrary Schubert class in H∗
(X, Z)
as a polynomial in certain special Schubert classes...
GROMOV-WITTEN INVARIANTS ON GRASSMANNIANS
GRASSMANNIANS GROMOV-WITTEN
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2015/12/17
We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a
two-step °ag variety. We also give symplectic and orthogonal...
QUANTUM COHOMOLOGY OF ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS QUANTUM COHOMOLOGY
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2015/12/17
Let V be a vector space with a nondegenerate symmetric form and
OG be the orthogonal Grassmannian which parametrizes maximal isotropic
subspaces in V . We give a presentation for the (small) quantum...
LITTLEWOOD-RICHARDSON RULES FOR GRASSMANNIANS
LITTLEWOOD-RICHARDSON GRASSMANNIANS special Schubert class
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2015/12/17
The classical Littlewood-Richardson rule [LR] describes the structure constants
obtained when the cup product of two Schubert classes in the cohomology ring of
a complex Grassmannian is written as a...
GROMOV-WITTEN INVARIANTS AND QUANTUM COHOMOLOGY OF GRASSMANNIANS
GROMOV-WITTEN INVARIANTS QUANTUM COHOMOLOGY
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2015/12/17
This is the written version of my ˉve lectures at the Banach Center
mini-school on `Schubert Varieties', in Warsaw, Poland, May 18{22, 2003.
QUANTUM COHOMOLOGY OF ISOTROPIC GRASSMANNIANS
ISOTROPIC GRASSMANNIANS QUANTUM
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2015/12/17
Let G be a classical Lie group and P a maximal parabolic subgroup. We describe a quantum Pieri rule which holds in the small quantum
cohomology ring of G=P. We also give a presentation of this ring i...
ARAKELOV THEORY OF EVEN ORTHOGONAL GRASSMANNIANS
GRASSMANNIANS ARAKELOV THEORY
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2015/12/17
We study the Arakelov intersection ring of the arithmetic scheme
OG which parametrizes maximal isotropic subspaces in an even dimensional
vector space, equipped with the standard hyperbolic quadrati...
QUANTUM PIERI RULES FOR ISOTROPIC GRASSMANNIANS
GRASSMANNIANS quantum
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2015/12/17
We study the three point genus zero Gromov-Witten invariants
on the Grassmannians which parametrize non-maximal isotropic subspaces in
a vector space equipped with a nondegenerate symmetric or skew-...
QUANTUM GIAMBELLI FORMULAS FOR ISOTROPIC GRASSMANNIANS
ISOTROPIC GRASSMANNIANS Vector space
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2015/12/17
Let X be a symplectic or odd orthogonal Grassmannian which
parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas ...
Singularities of duals of Grassmannians
Singularities of duals of Grassmannians Algebraic Geometry Differential Geometry
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2012/6/21
Let $X$ be a smooth irreducible nondegenerate projective variety and let $X^*$ denote its dual variety. It is well known that $\sigma_2(X)^*$, the dual of the 2-secant variety of $X$, is a component o...
Unitary grassmannians
Algebraic groups hermitian and quadratic forms projective homogeneous varieties Chow groups and motives
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2012/4/18
We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspa...
Incompressibility of orthogonal grassmannians
Algebraic groups quadratic forms projective homogeneous varieties Chow groups and motives
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2011/8/24
Abstract: We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary fiel...