Numerical Algorithms on the Affine Grassmannian
نویسندگان
چکیده
منابع مشابه
The Affine Grassmannian
The affine Grassmannian is an important object that comes up when one studies moduli spaces of the form BunG(X), where X is an algebraic curve and G is an algebraic group. There is a sense in which it describes the local geometry of such moduli spaces. I’ll describe the affine Grassmannian as a moduli space, and construct it concretely for some concrete groups. References, including the constru...
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Let G be a connected reductive group over C and let g be the Langlands dual Lie algebra. Crystals for g are combinatoral objects, that were introduced by Kashiwara (cf. for example [5]) as certain “combinatorial skeletons” of finite-dimensional representations of g. For every dominant weight λ of g Kashiwara constructed a crystal B(λ) by considering the corresponding finite-dimensional represen...
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We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C). Our main results are: • Pieri rules for the Schubert bases of H∗(Gr) and H∗(Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. • A new combinatorial definition for k-Schur functions, which represent the Schubert ba...
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This is the second paper of a series (started by [3]) which describes a conjectural analog of the affine Grassmannian for affine Kac-Moody groups (also known as the double affine Grassmannian). The current paper is dedicated to describing a conjectural analog of the convolution diagram for the double affine Grassmannian. In the case when G = SL(n) our conjectures can be derived from [12].
متن کاملSchubert Polynomials for the Affine Grassmannian
Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the k-Schur functions in homology and affine Schur functions in cohomology. Our results rely on Kostant and Kumar’s nilHecke ring, work of Peterson on the homology of based loops on a compact group, and earlier work of ours on non-commutative k-Schur functions.
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2019
ISSN: 0895-4798,1095-7162
DOI: 10.1137/18m1169321