Affine insertion and Pieri rules for the affine Grassmannian
نویسندگان
چکیده
منابع مشابه
Affine Insertion and Pieri Rules for the Affine Grassmannian
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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An explicit rule is given for the product of the degree two class with an arbitrary Schubert class in the torus-equivariant homology of the affine Grassmannian. In addition a Pieri rule (the Schubert expansion of the product of a special Schubert class with an arbitrary one) is established for the equivariant homology of the affine Grassmannians of SLn and a similar formula is conjectured for S...
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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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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: Memoirs of the American Mathematical Society
سال: 2010
ISSN: 0065-9266,1947-6221
DOI: 10.1090/s0065-9266-10-00576-4